---
title: "Translating Zelig to clarify"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Translating Zelig to clarify}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
bibliography: references.bib
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  warning = FALSE,
  fig.width = 6.5,
  fig.height = 2.75
)
```

## Introduction

In this document, we demonstrate some common uses of `Zelig` [@imaiCommonFrameworkStatistical2008a] and how the same tasks can be performed using `clarify`. We'll include examples for computing predictions at representative values (i.e., `setx()` and `sim()` in `Zelig`), the rare-events logit model, estimating the average treatment effect (ATT) after matching, and combining estimates after multiple imputation.

The usual workflow in `Zelig` is to fit a model using `zelig()`, specify quantities of interest to simulate using `setx()` on the `zelig()` output, and then simulate those quantities using `sim()`. `clarify` uses a similar approach, except that the model is fit outside `clarify` using functions in a different R package. In addition, `clarify`'s `sim_apply()` allows for the computation of any arbitrary quantity of interest. Unlike `Zelig`, `clarify` follows the recommendations of @raineyCarefulConsiderationCLARIFY2023 to use the estimates computed from the original model coefficients rather than the average of the simulated draws. We'll demonstrate how to replicate a standard `Zelig` analysis using `clarify` step-by-step. Because simulation-based inference involves randomness and some of the algorithms may not perfectly align, one shouldn't expect results to be identical, though in most cases, they should be similar.

```{r}
## library("Zelig")
library("clarify")
set.seed(100)
```

Note that both `Zelig` and `clarify` have a function called "`sim()`", so we will always make it clear which package's `sim()` is being used.

## Predictions at representative values

Here we'll use the `lalonde` dataset in `{MatchIt}` and fit a linear model for `re78` as a function of the treatment `treat` and covariates.

```{r}
data("lalonde", package = "MatchIt")
```

We'll be interested in the predicted values of the outcome for a typical unit at each level of treatment and their first difference.

### `Zelig` workflow

In `Zelig`, we fit the model using `zelig()`:

```{r, eval = FALSE}
fit <- zelig(re78 ~ treat + age + educ + married + race +
               nodegree + re74 + re75, data = lalonde,
             model = "ls", cite = FALSE)
```

Next, we use `setx()` and `setx1()` to set our values of `treat`:

```{r, eval = FALSE}
fit <- setx(fit, treat = 0)
fit <- setx1(fit, treat = 1)
```

Next we simulate the values using `sim()`:

```{r, eval = FALSE}
fit <- Zelig::sim(fit)
```

Finally, we can print and plot the predicted values and first differences:

```{r, eval = FALSE}
fit
```

```{r, eval = F}
plot(fit)
```

### `clarify` workflow

In `clarify`, we fit the model using functions outside `clarify`, like `stats::lm()`or `fixest::feols()`.

```{r}
fit <- lm(re78 ~ treat + age + educ + married + race +
            nodegree + re74 + re75, data = lalonde)
```

Next, we simulate the model coefficients using `clarify::sim()`:

```{r}
s <- clarify::sim(fit)
```

Next, we use `sim_setx()` to set our values of the predictors:

```{r}
est <- sim_setx(s, x = list(treat = 0), x1 = list(treat = 1),
                verbose = FALSE)
```

Finally, we can summarize and plot the predicted values:

```{r}
summary(est)

plot(est)
```

## Rare-events logit

`Zelig` uses a special method for logistic regression with rare events as described in @kingLogisticRegressionRare2001. This is the primary implementation of the method in R. However, newer methods have been developed that perform similarly to or better than the method of King and Zeng [@puhrFirthLogisticRegression2017] and are implemented in R packages that are compatible with `clarify`, such as `logistf` and `brglm2`.

Here, we'll use the `lalonde` dataset with a constructed rare outcome variable to demonstrate how to perform a rare events logistic regression in `Zelig` and in `clarify`.

```{r}
data("lalonde", package = "MatchIt")

#Rare outcome: 1978 earnings over $20k; ~6% prevalence
lalonde$re78_20k <- lalonde$re78 >= 20000
```

### `Zelig` workflow

In `Zelig`, we fit a rare events logistic model using `zelig()` with `model = "relogit"`.

```{r, eval = FALSE}
fit <- zelig(re78_20k ~ treat + age + educ + married + race +
               nodegree + re74 + re75, data = lalonde,
             model = "relogit", cite = FALSE)

fit
```

We can compute predicted values at representative values using `setx()` and `Zelig::sim()` as above.

```{r, eval = FALSE}
fit <- setx(fit, treat = 0)
fit <- setx1(fit, treat = 1)

fit <- Zelig::sim(fit)

fit
```

```{r, eval = FALSE}
plot(fit)
```

### `clarify` workflow

Here, we'll use `logistf::logistif()` with `flic = TRUE`, which performs a variation on Firth's logistic regression with a correction for bias in the intercept [@puhrFirthLogisticRegression2017].

```{r}
fit <- logistf::logistf(re78_20k ~ treat + age + educ + married + race +
                          nodegree + re74 + re75, data = lalonde,
                        flic = TRUE)

summary(fit)
```

We can compute predictions at representative values using `clarify::sim()` and `sim_setx()`.

```{r}
s <- clarify::sim(fit)

est <- sim_setx(s, x = list(treat = 0), x1 = list(treat = 1),
                verbose = FALSE)

summary(est)
```

```{r}
plot(est)
```

## Estimating the ATT after matching

Here we'll use the `lalonde` dataset and perform propensity score matching and then fit a linear model for `re78` as a function of the treatment `treat`, the covariates, and their interaction. From this model, we'll compute the ATT of `treat` using `Zelig` and `clarify`.

```{r}
data("lalonde", package = "MatchIt")

m.out <- MatchIt::matchit(treat ~ age + educ + married + race +
                            nodegree + re74 + re75, data = lalonde,
                          method = "nearest")
```

### `Zelig` workflow

In `Zelig`, we fit the model using `zelig()` directly on the `matchit` object:

```{r, eval = FALSE}
fit <- zelig(re78 ~ treat * (age + educ + married + race +
                               nodegree + re74 + re75),
             data = m.out, model = "ls", cite = FALSE)
```

Next, we use `ATT()` to request the ATT of `treat` and simulate the values:

```{r, eval = FALSE}
fit <- ATT(fit, "treat")
```

```{r, eval = F}
fit
```

```{r, eval = F}
plot(fit)
```

### `clarify` workflow

In `clarify`, we need to extract the matched dataset and fit a model outside `clarify` using another package.

```{r}
m.data <- MatchIt::match.data(m.out)

fit <- lm(re78 ~ treat * (age + educ + married + race +
                            nodegree + re74 + re75),
          data = m.data)
```

Next, we simulate the model coefficients using `clarify::sim()`. Because we performed pair matching, we will request a cluster-robust standard error:

```{r}
s <- clarify::sim(fit, vcov = ~subclass)
```

Next, we use `sim_ame()` to request the average marginal effect of `treat` within the subset of treated units:

```{r}
est <- sim_ame(s, var = "treat", subset = treat == 1,
               contrast = "diff", verbose = FALSE)
```

Finally, we can summarize and plot the ATT:

```{r}
summary(est)

plot(est)
```

## Combining results after multiple imputation

Here we'll use the `africa` dataset in `{Amelia}` to demonstrate combining estimates after multiple imputation. This analysis is also demonstrated using `clarify` at the end of `vignette("clarify")`.

```{r, message=F}
library(Amelia)
data("africa", package = "Amelia")
```

First we multiply impute the data using `amelia()` using the specification in the `{Amelia}` documentation.

```{r}
# Multiple imputation
a.out <- amelia(x = africa, m = 10, cs = "country",
                ts = "year", logs = "gdp_pc", p2s = 0)
```

### `Zelig` workflow

With `Zelig`, we can supply the `amelia` object directly to the `data` argument of `zelig()` to fit a model in each imputed dataset:

```{r, eval = FALSE}
fit <- zelig(gdp_pc ~ infl * trade, data = a.out,
             model = "ls", cite = FALSE)
```

Summarizing the coefficient estimates after the simulation can be done using `summary()`:

```{r, eval = FALSE}
summary(fit)
```

We can use `Zelig::sim()` and `setx()` to compute predictions at specified values of the predictors:

```{r, eval = FALSE}
fit <- setx(fit, infl = 0, trade = 40)
fit <- setx1(fit, infl = 0, trade = 60)

fit <- Zelig::sim(fit)
```

`Zelig` does not allow you to combine predicted values across imputations.

```{r, eval = F}
fit
```

```{r, eval = F}
plot(fit)
```

### `clarify` workflow

`clarify` does not combine coefficients, unlike `zelig()`; instead, the models should be fit using `Amelia::with()`. To view the combined coefficient estimates, use `Amelia::mi.combine()`.

```{r}
#Use Amelia functions to model and combine coefficients
fits <- with(a.out, lm(gdp_pc ~ infl * trade))

mi.combine(fits)
```

Derived quantities can be computed using `clarify::misim()` and `sim_apply()` or its wrappers on the `with()` output, which is a list of regression model fits:

```{r}
#Simulate coefficients, 100 in each of 10 imputations
s <- misim(fits, n = 100)

#Compute predictions at specified values
est <- sim_setx(s, x = list(infl = 0, trade = 40),
                x1 = list(infl = 0, trade = 60),
                verbose = FALSE)

summary(est)

plot(est)
```

## References
