Author: Gabriele Pittarello
Date: 2024-05-15

# Models comparison

#### Gabriele Pittarello

#### 2024-05-15

The `clmplus` package was created to provide actuarial scientists the tool-box that we illustrate in our paper, Pittarello G., Hiabu M., and Villegas A., Chain ladder Plus: a versatile approach for claims reserving, (pre-print, 2022). This vignette is made to make the readers able to recreate the type of analysis we make in the data application section of our paper. Please observe that the results we obtained in the paper were performed on a larger number of run-off triangles.

We believe it is extremely important to provide this vignette to disclose to the public the code we used to perform our analysis. Our results can be replicated by just running this vignette with the following seed. This vignette is organized as follows:

- In the bake-off section we provide numerical results to compare `clmplus` models performances to the `apc` package models performances on the test set.

- In the rankings section we try to rank `clmplus` models and the `apc` package models based on their performances on the validation set.

During the analysis we suggest how practitioners should split the data in order to perform the studies we just described.

For the case study in the paper we want to make our analysis as close as possible to a real life reserving problem. In order to do so, we decided to select data sets available to the public from the R packages `clmplus`, `ChainLadder`, and `apc`.

    list.of.datasets <- list(
      GenIns=GenIns,
      sifa.mod=sifa.mod,
      sifa.gtpl=sifa.gtpl,
      sifa.mtpl=sifa.mtpl,
      amases.gtpl=amases.gtpl,
      amases.mod=amases.mod,
      amases.mtpl=amases.mtpl,
      bz = incr2cum(data.loss.BZ()$response),
      ta = incr2cum(data.loss.TA()$response),
      xl = incr2cum(data.loss.XL()$response),
      vnj = incr2cum(data.loss.VNJ()$response),
      abc=ABC,
      autoC= auto$CommercialAutoPaid,
      autoP = auto$PersonalAutoPaid,
      autoBI = AutoBI$AutoBIPaid,
      mclpaid= MCLpaid,
      medmal=MedMal$MedMalPaid,
      mortgage=Mortgage,
      mw08=MW2008,
      mw14=MW2014,
      ukmotor = UKMotor,
      usapaid=USAApaid
    )

# Bake-off

Within this section we provide the code to measure the models extrapolation accuracy. In order to do so, we need to coherently split the data set into training, validation and testing. We show an example for a 12x12 run-off triangle.

    J=12
    df<-data.frame(expand.grid(c(0:(J-1)),c(0:(J-1))),c(1:(J^2)))
    colnames(df) <- c("origin","dev","value")
    df$value[df$origin+df$dev==(J-1)]=c(3)
    df$value[df$origin+df$dev<(J-2)]=c(1)
    df$value[df$origin+df$dev==(J-2)]=c(2)
    df$value[df$origin+df$dev>=J]=c(NA)
    #nas in the lower
    df[J,3]=c(NA)
    df[J-1,3]=c(NA)
    df[J+J-1,3]=c(NA)
    df[J*J-J+1,3]=c(NA)
    df[J*J-J+1,3]=c(NA)
    #nas in the upper tail
    df[J*J-J+1-12,3]=c(NA)
    df[J*J-J+2-12,3]=c(NA)

    ggplot(data=df, aes(x=as.integer(dev), y=as.integer(origin))) +
      geom_tile(aes(fill = as.factor(value),color="#000000"))+scale_y_reverse()+
      scale_fill_manual(values=c("royalblue", "darkred", "darkgreen","white"),
                        na.value = "white",
                        labels=c("Train","Validation","Test",""))+
      theme_classic()+
      labs(x="Development year", y="Accident year",fill="")+
      theme(axis.title.x = element_text(size=8), axis.text.x  = element_text(size=7))+
      theme(axis.title.y = element_text(size=8), axis.text.y  = element_text(size=7))+
      scale_color_brewer(guide = 'none')

    best.of.the.bests <- function(df1,df2){
      "
      Util to turn character columns values into numeric.
      "

      df1=apply(df1,MARGIN=2,FUN=as.numeric)
      df2=apply(df2,MARGIN=2,FUN=as.numeric)
      df3 <- rbind(df1,df2)
      df3=apply(df3,FUN=abs.min,MARGIN = 2)

      return(df3)

    }

    modelcomparison.1d <- function(cumulative.payments.triangle){
      "
      Function to compare the clmplus package age-period-cohort models with apc package age-period-cohort models  performances across different triangles.

      This function takes a triangle of cumulative payments as input.

      It returns the accuracy measures for the two families on the triangle.
      "
      # function internal variables

      leave.out=2

      rmse = NULL
      mae = NULL
      error.pc = NULL
      model.name = NULL
      error.incidence = NULL
      model.family = NULL
      mre = NULL

      # data pre-precessing ----

      J <- dim(cumulative.payments.triangle)[2]
      reduced.triangle <- c2t(t2c(cumulative.payments.triangle)[1:(J-leave.out),1:(J-leave.out)])
      newt.rtt <- AggregateDataPP(reduced.triangle)

      newt.apc <- apc.data.list(response=newt.rtt$incremental.payments.triangle,
                                data.format="CL")

      ## stmomo -----
      to.project <- t2c(cumulative.payments.triangle)[1:(J-leave.out-1),J-leave.out]
      true.values <- t2c(cumulative.payments.triangle)[2:(J-leave.out),(J-leave.out+1):J]

      for(ix in c('a','ac','ap','apc')){ ##names(models)

        hz.fit <- StMoMo::fit(models[[ix]],
                              Dxt = newt.rtt$occurrance,
                              Ext = newt.rtt$exposure,
                              wxt=newt.rtt$fit.w,
                              iterMax=as.integer(1e+05))
        hz.rate = fcst.fn(hz.fit,
                       hazard.model = ix,
                       gk.fc.model = 'a',
                       ckj.fc.model= 'a')$rates[,1:leave.out]

        J.new=dim(reduced.triangle)[2]
        fij = (2+hz.rate)/(2-hz.rate)
        pred.mx = fij
        pred.mx[,1]=fij[,1]*c(NA,to.project)
        temp=unname(pred.mx[1:(J.new-1),1][!is.na(pred.mx[1:(J.new-1),1])])
        pred.mx[,2]=fij[,2]*c(rep(NA,J.new-length(temp)),temp)
        true.mx= rbind(rep(NA,2),true.values)
        # this is meant to be NA
        true.mx[2,2]=NA

        sq.errors = (pred.mx-true.mx)^2
        abs.errors = abs(pred.mx-true.mx)
        r.errors = (pred.mx-true.mx)/true.mx
        error.inc.num = apply(pred.mx-true.mx,sum,MARGIN=2,na.rm=T)
        error.inc.den = apply(true.mx,sum,MARGIN=2,na.rm=T)
        model.name.ix = c(paste0(ix,".val"),paste0(ix,".test"))

        model.name = c(model.name,model.name.ix)
        model.family = c(model.family,rep(ix,2))
        rmse = c(rmse,sqrt(apply(sq.errors,MARGIN = 2,mean,na.rm=T)))
        mae = c(mae,apply(abs.errors,MARGIN = 2,mean,na.rm=T))
        mre = c(mre,apply(r.errors,MARGIN = 2,mean,na.rm=T))
        error.incidence = c(error.incidence,error.inc.num/error.inc.den)

      }

      ## stmomo results ----

       out1 <- data.frame(
        model.name,
        model.family,
        mre,
        error.incidence,
        rmse,
        mae)

      temp.ix <- grepl(".val", model.name)
      temp.df <- out1[temp.ix,]

      out2 <- data.frame(
        rmse=temp.df$model.name[which(abs(temp.df$rmse)==min(abs(temp.df$rmse)))],
        mre=temp.df$model.name[which(abs(temp.df$mre)==min(abs(temp.df$mre)))],
        mae=temp.df$model.name[which(abs(temp.df$mae)==min(abs(temp.df$mae)))],
        error.incidence=temp.df$model.name[which(abs(temp.df$error.incidence)==min(abs(temp.df$error.incidence)))])

      temp.ix <- grepl(".test", model.name)
      out3 <- out1[temp.ix,]

      best.df = out2
      best.df[1,]=NA

      out.test.min <- data.frame(
        rmse=out3$model.name[which(abs(out3$rmse)==min(abs(out3$rmse)))],
        mre=out3$model.name[which(abs(out3$mre)==min(abs(out3$mre)))],
        mae=out3$model.name[which(abs(out3$mae)==min(abs(out3$mae)))],
        error.incidence=out3$model.name[which(abs(out3$error.incidence)==min(abs(out3$error.incidence)))])

      temp.mx=matrix((sub("\\..*", "", out2) == sub("\\..*", "", out.test.min)),nrow=1)
      choices.mx.clmplus=matrix(sub("\\..*", "", out2),nrow=1)

      agreement.frame.clmplus=data.frame(temp.mx)
      choices.frame.clmplus=data.frame(choices.mx.clmplus)

      colnames(agreement.frame.clmplus)=colnames(out2)
      colnames(choices.frame.clmplus)=colnames(out2)

      for(col.ix in colnames(out2)){

      res=out1$model.family[out1$model.name == out2[1,col.ix]]
      res.test = out3$model.family == res
      best.df[1,col.ix] = out3[res.test,col.ix]}

      families.set=c('a','apc') #'ap',
      temp.ix = out3$model.family %in% families.set
      comparison.df = out3[temp.ix,]
      comparison.df = cbind(comparison.df,
                            approach=rep('clmplus',length(families.set)))

      ## apc ----

      rmse = NULL
      mae = NULL
      error.pc = NULL
      model.name = NULL
      error.incidence = NULL
      model.family = NULL
      mre = NULL

      true.inc.values <- t2c(cum2incr(cumulative.payments.triangle))[2:(J-leave.out),(J-leave.out+1):J]

      for(apc.mods in c("AC","APC")){ #,"AP"

        fit <- apc.fit.model(newt.apc,
                             model.family = "od.poisson.response",
                             model.design = apc.mods)

        if(apc.mods == "AC"){fcst <- apc.forecast.ac(fit)$trap.response.forecast}
        # if(apc.mods == "AP"){fcst <- apc.forecast.ap(fit)$trap.response.forecast}
        if(apc.mods == "APC"){fcst <- apc.forecast.apc(fit)$trap.response.forecast}

        plogram.hat = t2c.full.square(incr2cum(t(fcst)))
        pred.mx = plogram.hat[,(J-leave.out+1):J]

        # true.mx= rbind(rep(NA,2),true.inc.values)
        # # this is meant to be NA
        # true.mx[2,2]=NA

        sq.errors = (pred.mx-true.mx)^2
        abs.errors = abs(pred.mx-true.mx)
        r.errors = (pred.mx-true.mx)/true.mx #use same benchmark
        error.inc.num = apply(pred.mx-true.mx,sum,MARGIN=2,na.rm=T)
        error.inc.den = apply(true.mx,sum,MARGIN=2,na.rm=T) #use same benchmark
        model.name.ix = c(paste0(apc.mods,".val"),paste0(apc.mods,".test"))

        model.name = c(model.name,tolower(model.name.ix))
        model.family = c(model.family,tolower(rep(apc.mods,2)))
        rmse = c(rmse,sqrt(apply(sq.errors,MARGIN = 2,mean,na.rm=T)))
        mae = c(mae,apply(abs.errors,MARGIN = 2,mean,na.rm=T))
        mre = c(mre,apply(r.errors,MARGIN = 2,mean,na.rm=T))
        error.incidence = c(error.incidence,error.inc.num/error.inc.den)}

       out4 <- data.frame(
        model.name,
        model.family,
        mre,
        error.incidence,
        rmse,
        mae)

      temp.ix <- grepl(".val", model.name)
      temp.df <- out4[temp.ix,]

      out5 <- data.frame(
        rmse=temp.df$model.name[which(abs(temp.df$rmse)==min(abs(temp.df$rmse)))],
        mre=temp.df$model.name[which(abs(temp.df$mre)==min(abs(temp.df$mre)))],
        mae=temp.df$model.name[which(abs(temp.df$mae)==min(abs(temp.df$mae)))],
        error.incidence=temp.df$model.name[which(abs(temp.df$error.incidence)==min(abs(temp.df$error.incidence)))])

      temp.ix <- grepl(".test", model.name)
      out6 <- out4[temp.ix,]

      out.test.min2 <- data.frame(
      rmse=out6$model.name[which(abs(out6$rmse)==min(abs(out6$rmse)))],
      mre=out6$model.name[which(abs(out6$mre)==min(abs(out6$mre)))],
      mae=out6$model.name[which(abs(out6$mae)==min(abs(out6$mae)))],
      error.incidence=out6$model.name[which(abs(out6$error.incidence)==min(abs(out6$error.incidence)))])

      temp.mx=matrix((sub("\\..*", "", out5) == sub("\\..*", "", out.test.min2)),nrow=1)
      choices.mx.apc=matrix(sub("\\..*", "", out5),nrow=1)

      choices.frame.apc=data.frame(choices.mx.apc)
      agreement.frame.apc=data.frame(temp.mx)

      colnames(agreement.frame.apc)=colnames(out5)
      colnames(choices.frame.apc)=colnames(out5)

      best.df.apc = out5
      best.df.apc[1,]=NA

      for(col.ix in colnames(out5)){

      res=out4$model.family[out4$model.name == out5[1,col.ix]]
      res.test = out6$model.family == res
      best.df.apc[1,col.ix] = out6[res.test,col.ix]}

      families.set=c('ac','apc') #'ap',
      temp.ix = out6$model.family %in% families.set
      comparison.df.apc = out6[temp.ix,]
      comparison.df.apc = cbind(comparison.df.apc,
                                approach=rep('apc',length(families.set)))

      out = list(
        best.model.clmplus = best.df,
        best.model.apc = best.df.apc,
        agreement.frame.clmplus=agreement.frame.clmplus,
        agreement.frame.apc=agreement.frame.apc,
        choices.frame.clmplus=choices.frame.clmplus,
        choices.frame.apc=choices.frame.apc,
        comparison.df = rbind(comparison.df,
                              comparison.df.apc))

      return(out)}

    modelcomparison<-function(list.of.datasets){
      "This functions returns the datasets to plot the bake-off section of the paper.

      The input is a list of datasets that constitue the sample.

      The output is datasets that contain accuracy measures.

      "
      best.fit=NULL
      families.fit=NULL
      agreement.clmplus=NULL
      agreement.apc=NULL
      choices.clmplus=NULL
      choices.apc=NULL

      for(df.ix in names(list.of.datasets)){
        cat(paste0(".. Comparison on dataset: ",df.ix))
        out.ix = modelcomparison.1d(list.of.datasets[[df.ix]])

        best.of.the.bests.df=best.of.the.bests(out.ix$best.model.clmplus,
                                            out.ix$best.model.apc)

        out.ix$best.model.clmplus['package']= 'clmplus'
        out.ix$best.model.apc['package']= 'apc'
        best.of.the.bests.df['package']='overall.best'

        best.fit=rbind(best.fit,
                       out.ix$best.model.clmplus,
                       out.ix$best.model.apc,
                       best.of.the.bests.df)

        families.fit=rbind(families.fit,
                       out.ix$comparison.df)

        agreement.clmplus=rbind(agreement.clmplus,
                             out.ix$agreement.frame.clmplus)

        agreement.apc=rbind(agreement.apc,
                             out.ix$agreement.frame.apc)

        choices.clmplus=rbind(choices.clmplus,
                             out.ix$choices.frame.clmplus)

        choices.apc=rbind(choices.apc,
                             out.ix$choices.frame.apc)
      }

      best.fit[,1:4]=apply(best.fit[,1:4],MARGIN = 2,FUN = as.numeric)

      families.fit[,c('mre',
                      'error.incidence',
                      'rmse',
                      'mae')]=apply(
                        families.fit[,c('mre',
                                        'error.incidence',
                                        'rmse',
                                        'mae')],
                        MARGIN = 2,
                        FUN = as.numeric)

      out = list(best.fit=best.fit,
                 families.fit=families.fit,
                 agreement.clmplus=agreement.clmplus,
                 agreement.apc=agreement.apc,
                 choices.clmplus=choices.clmplus,
                 choices.apc=choices.apc)

      return(out)

    }

    bake.off <- function(models.comparison){
      "
      This function plots out the results from the previous computations.

      It takes as input the resulting dataframes of model.comparison.

      The output is the boxplots of the paper's bake-off section.

      "

      p1<- models.comparison$best.fit[,c("rmse","mae","package")] %>%
        tidyr::pivot_longer(-c(package)) %>%
        ggplot(aes(x=package,y=value))+
        geom_boxplot()+
        facet_wrap(.~name,nrow = 1,strip.position = 'bottom')+
        theme_bw()+
        theme(strip.placement = 'outside',strip.background = element_blank())

      p2<- models.comparison$best.fit[,c("mre","error.incidence","package")] %>%
        tidyr::pivot_longer(-c(package)) %>%
        ggplot(aes(x=package,y=value))+
        geom_boxplot()+
        facet_wrap(.~name,nrow = 1,strip.position = 'bottom')+
        theme_bw()+
        theme(strip.placement = 'outside',strip.background = element_blank())

      abs.best=models.comparison$best.fit[,c("mre","error.incidence","package")]
      abs.best[,c("mre","error.incidence")]=apply(abs.best[,c("mre","error.incidence")],
                                                  MARGIN=2,
                                                  FUN=abs)
      p3<- abs.best %>%
        tidyr::pivot_longer(-c(package)) %>%
        ggplot(aes(x=package,y=value))+
        geom_boxplot()+
        facet_wrap(.~name,nrow = 1,strip.position = 'bottom')+
        theme_bw()+
        theme(strip.placement = 'outside',strip.background = element_blank())

      only.ei=models.comparison$best.fit[,c("error.incidence","package")]
      only.ei[,c("error.incidence")]=abs(only.ei[,c("error.incidence")])

      p4<- abs.best %>%
      tidyr::pivot_longer(-c(package)) %>%
      ggplot(aes(x=package,y=value))+
      geom_boxplot()+
      # facet_wrap(.~name,nrow = 1,strip.position = 'bottom')+
      theme_bw()+
      theme(strip.placement = 'outside',strip.background = element_blank())

      out = list(p1=p1,
                 p2=p2,
                 p3=p3,
                 p4=p4)

      return(out)
    }

The models in the `clmplus` package are compared to those in the `apc` package. Below it can be found the code we used to create the bake-off plot in our paper.

    out=modelcomparison(list.of.datasets = list.of.datasets)
    #> .. Comparison on dataset: GenIns
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: sifa.mod
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: sifa.gtpl
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: sifa.mtpl
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 860.063891
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49353.589600
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 29251.193380
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 36106.295210
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 40125.390780
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 44498.942240
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 45490.189570
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 48040.321560
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49991.357650
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49694.294990
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 20880.666980
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12463.983790
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 13441.333110
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12951.176400
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15370.423630
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15339.426370
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 17842.901760
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 19570.203660
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 10047.067150
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5144.085289
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5868.234632
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 6033.755464
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5593.853546
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5478.076757
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 7035.199194
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3933.606063
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2726.947823
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2881.972323
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3009.655856
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2615.516340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2540.639658
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2906.368627
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2359.362462
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2421.987896
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1264.396267
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1984.311792
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2136.804699
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1333.856105
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 918.004039
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1249.952517
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1134.706143
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1238.429974
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1075.978340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 733.741025
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 941.440475
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 860.063891
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49353.589600
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 29251.193380
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 36106.295210
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 40125.390780
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 44498.942240
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 45490.189570
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 48040.321560
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49991.357650
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49694.294990
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 20880.666980
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12463.983790
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 13441.333110
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12951.176400
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15370.423630
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15339.426370
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 17842.901760
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 19570.203660
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 10047.067150
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5144.085289
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5868.234632
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 6033.755464
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5593.853546
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5478.076757
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 7035.199194
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3933.606063
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2726.947823
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2881.972323
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3009.655856
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2615.516340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2540.639658
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2906.368627
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2359.362462
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2421.987896
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1264.396267
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1984.311792
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2136.804699
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1333.856105
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 918.004039
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1249.952517
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1134.706143
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1238.429974
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1075.978340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 733.741025
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 941.440475
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 860.063891
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49353.589600
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 29251.193380
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 36106.295210
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 40125.390780
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 44498.942240
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 45490.189570
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 48040.321560
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49991.357650
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49694.294990
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 20880.666980
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12463.983790
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 13441.333110
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12951.176400
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15370.423630
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15339.426370
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 17842.901760
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 19570.203660
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 10047.067150
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5144.085289
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5868.234632
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 6033.755464
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5593.853546
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5478.076757
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 7035.199194
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3933.606063
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2726.947823
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2881.972323
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3009.655856
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2615.516340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2540.639658
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2906.368627
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2359.362462
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2421.987896
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1264.396267
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1984.311792
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2136.804699
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1333.856105
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 918.004039
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1249.952517
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1134.706143
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1238.429974
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1075.978340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 733.741025
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 941.440475
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 860.063891
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49353.589600
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 29251.193380
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 36106.295210
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 40125.390780
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 44498.942240
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 45490.189570
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 48040.321560
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49991.357650
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49694.294990
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 20880.666980
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12463.983790
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 13441.333110
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12951.176400
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15370.423630
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15339.426370
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 17842.901760
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 19570.203660
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 10047.067150
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5144.085289
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5868.234632
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 6033.755464
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5593.853546
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5478.076757
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 7035.199194
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3933.606063
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2726.947823
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2881.972323
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3009.655856
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2615.516340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2540.639658
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2906.368627
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2359.362462
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2421.987896
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1264.396267
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1984.311792
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2136.804699
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1333.856105
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 918.004039
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1249.952517
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1134.706143
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1238.429974
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1075.978340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 733.741025
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 941.440475
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: amases.gtpl
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: amases.mod
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: amases.mtpl
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: bz
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: ta
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: xl
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 153 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 17
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 153 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 17
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 153 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 17
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 153 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 17
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: vnj
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: abc
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: autoC
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: autoP
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: autoBI
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: mclpaid
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 10 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -4 -3 -2 -1 4
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 10 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -4 -3 -2 -1 4
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 10 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -4 -3 -2 -1 4
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 10 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -4 -3 -2 -1 4
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: medmal
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: mortgage
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: mw08
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: mw14
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 105 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 14
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 105 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 14
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 105 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 14
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 105 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 14
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: ukmotor
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 10 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -4 -3 -2 -1 4
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 10 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -4 -3 -2 -1 4
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 10 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -4 -3 -2 -1 4
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 10 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -4 -3 -2 -1 4
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> .. Comparison on dataset: usapaid
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm

    cake = bake.off(out)

    cake$p3

In detail, having the three set at disposal, for each case we are able to pick the best model based on the error incidence.

    abs.best=out$best.fit[,c("error.incidence","package")]
    abs.best[,c("error.incidence")]=abs(abs.best[,c("error.incidence")])
    abs.best[,'data.source']=sort(rep(seq(1,dim(abs.best)[1]/3),3))

    p3<- ggplot(abs.best,aes(x=package,
                             y=error.incidence,
                             fill=package,
                             label=data.source)) +
      geom_boxplot(outlier.shape = NA)+
      viridis::scale_fill_viridis(discrete=T, alpha=0.6) +
      geom_jitter(color="black",
                  size=1,
                  alpha=0.9,
                  position = position_jitter(seed = 1)) +
      geom_text(aes(label=ifelse(data.source%in% c(15,24,17,18),
                       as.character(data.source),'')),
      hjust=0,
      vjust=0,
      size=5,
      position = position_jitter(seed = 1))+
      # geom_text(position = position_jitter(seed = 42))+
      coord_flip()+
      theme_bw()+
      ggplot2::labs(x="Package", y="Error Incidence")+
      theme(axis.text.y = element_text(size=15),
            axis.text.x  = element_text(size=15))+
      theme(axis.title.y = element_text(size=20),
            axis.title.x  = element_text(size=20))

    p3

# Rankings

Within this section we provide practitioners with the code to perform models ranking. Now we have a different training validation split. The training validation split we use is represented in the following picture.

    # models ranking

    J=12
    df<-data.frame(expand.grid(c(0:(J-1)),c(0:(J-1))),c(1:(J^2)))
    colnames(df) <- c("origin","dev","value")
    df$value[df$origin+df$dev==(J-1)]=c(2)
    df$value[df$origin+df$dev<(J-1)]=c(1)
    df$value[df$origin+df$dev>=J]=c(NA)
    df[J,3]=c(NA)
    df[J*J-J+1,3]=c(NA)

    ggplot(data=df, aes(x=as.integer(dev), y=as.integer(origin))) +
      geom_tile(aes(fill = as.factor(value),color="#000000"))+scale_y_reverse()+
      scale_fill_manual(values=c("royalblue", "darkred", "white"),
                        na.value = "white",
                        labels=c("Train","Validation",""))+
      theme_classic()+
      labs(x="Development year", y="Accident year",fill="")+
      theme(axis.title.x = element_text(size=8), axis.text.x  = element_text(size=7))+
      theme(axis.title.y = element_text(size=8), axis.text.y  = element_text(size=7))+
      scale_color_brewer(guide = 'none')

    modelsranking.1d <- function(data.T){
      "
      Function to rank the clmplus package and apc package age-period-cohort models.

      This function takes a triangle of cumulative payments as input.

      It returns the ranking on the triangle.
      "

      leave.out=1

      model.name = NULL
      error.incidence = NULL
      mre = NULL

      #pre-processing
      triangle <- data.T$cumulative.payments.triangle
      J <- dim(triangle)[2]
      reduced.triangle <- c2t(t2c(triangle)[1:(J-leave.out),1:(J-leave.out)])
      newt.rtt <- AggregateDataPP(reduced.triangle)
      to.project <- t2c(triangle)[1:(J-leave.out-1),J-leave.out]
      true.values <- t2c(triangle)[2:(J-leave.out),J]

      for(ix in c('a','ac','ap','apc')){

        hz.fit <- StMoMo::fit(models[[ix]],
                              Dxt = newt.rtt$occurrance,
                              Ext = newt.rtt$exposure,
                              wxt=newt.rtt$fit.w,
                              iterMax=as.integer(1e+05))
        hz.rate = fcst.fn(hz.fit,
                       hazard.model = ix,
                       gk.fc.model = 'a',
                       ckj.fc.model= 'a')$rates[,1]

        fij = (2+hz.rate)/(2-hz.rate)
        pred.fij = fij[(leave.out+1):length(fij)]
        pred.v=to.project*pred.fij

        r.errors = (pred.v-true.values)/true.values
        error.inc.num = sum(pred.v-true.values,na.rm = T)
        error.inc.den = sum(true.values)

        model.name = c(model.name,
                       paste0('clmplus.',ix))
        error.incidence = c(error.incidence,error.inc.num/error.inc.den)
        mre = c(mre,mean(r.errors))

      }

      # ix='lc'
      # hz.fit <- fit.lc.nr(data.T = newt.rtt,
      #                     iter.max = 3e+04)
      # if(hz.fit$converged==TRUE){hz.rate = forecast.lc.nr(hz.fit,J=dim(newt.rtt$cumulative.payments.triangle)[2])$rates[,1:leave.out]
      # fij = (2+hz.rate)/(2-hz.rate)
      # pred.fij = fij[(leave.out+1):length(fij)]
      # pred.v=to.project*pred.fij
      # r.errors = (pred.v-true.values)/true.values
      #
      # error.inc.num = sum(pred.v-true.values,na.rm = T)
      # error.inc.den = sum(true.values)
      #
      # model.name = c(model.name,
      #                paste0('clmplus.',ix))
      # error.incidence = c(error.incidence,error.inc.num/error.inc.den)
      # mre = c(mre,mean(r.errors))}

      out1 <- data.frame(
        model.name,
        # mre,
        error.incidence)

      ## APC package

      newt.apc <- apc.data.list(response=newt.rtt$incremental.payments.triangle,
                                data.format="CL")

      ## apc

      rmse = NULL
      mae = NULL
      error.pc = NULL
      model.name = NULL
      error.incidence = NULL
      model.family = NULL
      mre = NULL

      true.inc.values <- t2c(data.T$incremental.payments.triangle)[2:(J-leave.out),(J-leave.out+1):J]

      for(apc.mods in c("AC","APC")){ #,"AP"

        fit <- apc.fit.model(newt.apc,
                             model.family = "od.poisson.response",
                             model.design = apc.mods)

        if(apc.mods == "AC"){fcst <- apc.forecast.ac(fit)$trap.response.forecast}
        # if(apc.mods == "AP"){fcst <- apc.forecast.ap(fit)$trap.response.forecast}
        if(apc.mods == "APC"){fcst <- apc.forecast.apc(fit)$trap.response.forecast}

        plogram.hat = t2c.full.square(incr2cum(t(fcst)))
        pred.v = plogram.hat[,(J-leave.out+1):J]
        pred.v = pred.v[2:length(pred.v)]

        r.errors = (pred.v-true.values)/true.values
        error.inc.num = sum(pred.v-true.values)
        error.inc.den = sum(true.values)

        model.name = c(model.name,
                       paste0('apc.',tolower(apc.mods)))
        error.incidence = c(error.incidence,error.inc.num/error.inc.den)
        mre = c(mre,mean(r.errors))

      }

      out2 <- data.frame(
        model.name,
        # mre,
        error.incidence)

      out3 <- rbind(out1,out2)

      out3 <- out3[order(abs(out3$error.incidence),decreasing = F),]
      out3[,'ei.rank']=c(1:dim(out3)[1])
      # out3[,'mre.rank']=order(abs(out3$mre),decreasing = F)
      #fix it manually
      r2set=min(out3$ei.rank[out3$model.name=='apc.ac'],
                out3$ei.rank[out3$model.name=='clmplus.a'])

      out3$ei.rank[out3$model.name=='apc.ac']=r2set
      out3$ei.rank[out3$model.name=='clmplus.a']=r2set

      if( out3$ei.rank[out3$model.name=='apc.ac'] < max(out3$ei.rank)){
        cond=out3$ei.rank>out3$ei.rank[out3$model.name=='apc.ac']
        out3$ei.rank[cond]=out3$ei.rank[cond]-1
      }

      return(list(models.ranks=out3))

    }

    modelsranking <- function(list.of.datasets){

      "
      This functions returns the datasets to plot in the ranking section of the paper.

      The input is a list of datasets that constitue the sample.

      The output is the rankings across different data sources.
      "

      full.ranks=NULL

      for(df.ix in names(list.of.datasets)){

        out.df=modelsranking.1d(AggregateDataPP(list.of.datasets[[df.ix]]))
        out.df$models.ranks[,'data.source']=rep(df.ix,dim(out.df$models.ranks)[1])
        full.ranks=rbind(full.ranks,out.df$models.ranks)
      }

      return(list(full.ranks=full.ranks))
    }

    full.ranks=modelsranking(list.of.datasets)
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 860.063891
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 458.156066
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 281.869679
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49353.589600
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 50605.820000
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 29251.193380
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 36106.295210
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 40125.390780
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 44498.942240
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 45490.189570
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 48040.321560
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49991.357650
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49694.294990
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 20880.666980
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 18304.246140
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12463.983790
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 13441.333110
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12951.176400
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15370.423630
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15339.426370
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 17842.901760
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 19570.203660
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 10047.067150
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 8201.559214
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5144.085289
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5868.234632
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 6033.755464
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5593.853546
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5478.076757
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 7035.199194
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3933.606063
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5749.890057
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2726.947823
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2881.972323
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3009.655856
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2615.516340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2540.639658
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2906.368627
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2725.682936
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2359.362462
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2421.987896
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1264.396267
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1984.311792
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2136.804699
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1294.338023
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1333.856105
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 918.004039
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1249.952517
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1134.706143
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1184.355428
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1238.429974
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1075.978340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 733.741025
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 904.371165
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 941.440475
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 860.063891
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 458.156066
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 281.869679
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49353.589600
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 50605.820000
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 29251.193380
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 36106.295210
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 40125.390780
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 44498.942240
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 45490.189570
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 48040.321560
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49991.357650
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49694.294990
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 20880.666980
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 18304.246140
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12463.983790
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 13441.333110
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12951.176400
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15370.423630
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15339.426370
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 17842.901760
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 19570.203660
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 10047.067150
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 8201.559214
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5144.085289
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5868.234632
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 6033.755464
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5593.853546
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5478.076757
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 7035.199194
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3933.606063
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5749.890057
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2726.947823
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2881.972323
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3009.655856
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2615.516340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2540.639658
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2906.368627
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2725.682936
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2359.362462
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2421.987896
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1264.396267
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1984.311792
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2136.804699
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1294.338023
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1333.856105
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 918.004039
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1249.952517
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1134.706143
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1184.355428
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1238.429974
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1075.978340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 733.741025
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 904.371165
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 941.440475
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 860.063891
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 458.156066
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 281.869679
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49353.589600
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 50605.820000
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 29251.193380
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 36106.295210
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 40125.390780
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 44498.942240
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 45490.189570
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 48040.321560
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49991.357650
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49694.294990
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 20880.666980
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 18304.246140
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12463.983790
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 13441.333110
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12951.176400
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15370.423630
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15339.426370
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 17842.901760
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 19570.203660
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 10047.067150
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 8201.559214
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5144.085289
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5868.234632
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 6033.755464
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5593.853546
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5478.076757
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 7035.199194
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3933.606063
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5749.890057
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2726.947823
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2881.972323
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3009.655856
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2615.516340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2540.639658
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2906.368627
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2725.682936
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2359.362462
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2421.987896
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1264.396267
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1984.311792
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2136.804699
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1294.338023
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1333.856105
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 918.004039
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1249.952517
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1134.706143
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1184.355428
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1238.429974
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1075.978340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 733.741025
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 904.371165
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 941.440475
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 860.063891
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 458.156066
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 281.869679
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49353.589600
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 50605.820000
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 29251.193380
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 36106.295210
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 40125.390780
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 44498.942240
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 45490.189570
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 48040.321560
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49991.357650
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 49694.294990
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 20880.666980
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 18304.246140
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12463.983790
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 13441.333110
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 12951.176400
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15370.423630
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 15339.426370
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 17842.901760
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 19570.203660
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 10047.067150
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 8201.559214
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5144.085289
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5868.234632
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 6033.755464
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5593.853546
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5478.076757
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 7035.199194
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3933.606063
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 5749.890057
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2726.947823
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2881.972323
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 3009.655856
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2615.516340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2540.639658
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2906.368627
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2725.682936
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2359.362462
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2421.987896
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1264.396267
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1984.311792
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 2136.804699
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1294.338023
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1333.856105
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 918.004039
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1249.952517
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1134.706143
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1184.355428
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1238.429974
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 1075.978340
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 733.741025
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 904.371165
    #> Warning in dpois(y, mu, log = TRUE): non-integer x = 941.440475
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 55 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 171 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 18
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 171 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 18
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 171 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 18
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 171 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 18
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 45 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -9 -8 -7 -6 -5 -4 -3 -2 -1 9
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 21 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -6 -5 -4 -3 -2 -1 6
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 28 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -7 -6 -5 -4 -3 -2 -1 7
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 120 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 15
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 120 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 15
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 120 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 15
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 120 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 15
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 15 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -5 -4 -3 -2 -1 5
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm
    #> Warning in fit.StMoMo(models[[ix]], Dxt = newt.rtt$occurrance, Ext = newt.rtt$exposure, : StMoMo: 36 missing values which have been zero weighted
    #> StMoMo: The following ages have been zero weigthed: 1
    #> StMoMo: The following years have been zero weigthed: 1
    #> StMoMo: The following cohorts have been zero weigthed: -8 -7 -6 -5 -4 -3 -2 -1 8
    #> StMoMo: Start fitting with gnm
    #> StMoMo: Finish fitting with gnm

The following picture is the models ranks plot we included in the paper.

    p_min_expd0 <- ggplot(full.ranks$full.ranks, aes(model.name, data.source)) +
       geom_tile(aes(fill = cut(ei.rank, breaks=0:6, labels=1:6)), colour = "grey") +
       ggtitle(" ") +
      theme_classic()+
      geom_text(aes(label = ei.rank))+
       scale_y_discrete(limits=names(list.of.datasets)) +
       scale_fill_manual(drop=FALSE, values=colorRampPalette(c("white","#6699CC"))(6), na.value="#EEEEEE", name="Rank") +
       xlab("Model") + ylab("Data source")
    p_min_expd0

It can be useful to inspect the average rank of the different models we were comparing.

    tbl=full.ranks$full.ranks %>%
      dplyr::group_by(model.name) %>%
      dplyr::summarise(mean.rank = mean(ei.rank))
    tbl
    #> # A tibble: 6 × 2
    #>   model.name  mean.rank
    #>   <chr>           <dbl>
    #> 1 apc.ac           3.09
    #> 2 apc.apc          4.14
    #> 3 clmplus.a        3.09
    #> 4 clmplus.ac       2.32
    #> 5 clmplus.ap       3
    #> 6 clmplus.apc      2.45

    library(dplyr)
    temp.df=full.ranks$full.ranks[,c('model.name','ei.rank')] %>%
      group_by(model.name, ei.rank) %>% summarise(count = n())
    #> `summarise()` has grouped output by 'model.name'. You can override using the
    #> `.groups` argument.

The following picture was not included in the paper but it shows the models ranks counts. It provides additional consistency to the results we included in our work.

    ggplot(temp.df, aes(y=count, x=factor(ei.rank))) +
        geom_bar(position="stack", stat="identity",fill='#6699CC') +
      scale_y_continuous(limits=c(0,15))+
      facet_wrap(~model.name, scales='free')+
      theme_classic()+
      ylab("")+
      xlab("Rank")

# Conclusions

In this vignette we wanted to show how the tool-box of actuarial scientists is enriched thanks to `clmplus`.

- It is important to perform different analysis to validate results. In this work we showed two.

- There is no best model in absolute terms: our purpose is to show that more options can improve claims reserving.