# Observation influence audit

## Alicja Gosiewska

### 2023-10-29

Observation influence audit, i.e. the impact of individual observation on a model.

## Data

To illustrate application of `auditor` we will use dataset “dragons” available in the `DALEX` package. The dataset contains characteristics of fictional creatures (dragons), like year of birth, height, weight, etc (see below). The goal is to predict the length of life of dragons (a regression problem).

    library(DALEX)
    data(dragons)
    head(dragons)

    ##   year_of_birth   height   weight scars colour year_of_discovery
    ## 1         -1291 59.40365 15.32391     7    red              1700
    ## 2          1589 46.21374 11.80819     5    red              1700
    ## 3          1528 49.17233 13.34482     6    red              1700
    ## 4          1645 48.29177 13.27427     5  green              1700
    ## 5            -8 49.99679 13.08757     1    red              1700
    ## 6           915 45.40876 11.48717     2    red              1700
    ##   number_of_lost_teeth life_length
    ## 1                   25   1368.4331
    ## 2                   28   1377.0474
    ## 3                   38   1603.9632
    ## 4                   33   1434.4222
    ## 5                   18    985.4905
    ## 6                   20    969.5682

## Models

First, we need models to compare. We selected linear regression and random forest because of their different structures. Linear regression model linear relationships between target response and independent variables. While random forest should be able to capture also non-linear relationships between variables.

    # Linear regression
    lm_model <- lm(life_length ~ ., data = dragons)

    # Random forest
    library(randomForest)
    set.seed(59)
    rf_model <- randomForest(life_length ~ ., data = dragons)

## Preparation for analysis of observation influence

Analysis begins with creation of an explainer object with `explain` function from `DALEX` package. Explainer wraps a model with its meta-data, such as dataset that was used for training or observed response.

    lm_exp <- DALEX::explain(lm_model, label = "lm", data = dragons, y = dragons$life_length)
    rf_exp <- DALEX::explain(rf_model, label = "rf", data = dragons, y = dragons$life_length)

Next step requires creation of `model_cooksdistance` objects of each explained model. In the case of models of classes other than `lm` and `glm`, the distances are computed directly from the definition, so this may take a while. In this example we will compute them only for a linear model.

    library(auditor)
    lm_cd <- model_cooksdistance(lm_exp)

## Plot of Cook’s distances

Cook’s distance is used to estimate of the influence of an single observation. It is a tool for identifying observations that may negatively affect the model.

Data points indicated by Cook’s distances are worth checking for validity. Cook’s distances may be also used for indicating regions of the design space where it would be good to obtain more observations.

Cook’s Distances are calculated by removing the i-th observation from the data and recalculating the model. It shows how much all the values in the model change when the i-th observation is removed.

    plot(lm_cd)

## Other methods

Other methods and plots are described in following vignettes:

- Model residuals audit
- Model evaluation audit
- Model fit audit
- Model performance audit