10_ceteris-paribus-profiles.Rmd

# Ceteris-paribus Profiles

**Learning objectives:**

-   Definition of CP profiles
-   CP visualization and methodology
-   Examine CP profiles using the Titanic imputed dataset
-   Pros and cons

## Introduction

-   *Ceteris Paribus* is a Latin phrase meaning "other things held constant" or "all else unchanged".
-   *Ceteris paribus* profiles, or CP profiles, show how one variable affects the outcome, holding all other variables fixed, for one observation.

## Intuition

-   In essence, a CP profile shows the dependence of the conditional expectation of the dependent variable (response) on the values of the particular explanatory variable.

-   Figure 10.1 Panel A presents a 3D visualization, where $x$ is the `age`, $y$ is the response (prediction probability), and $z$ is the `class` factor for the 'titanic_lmr' logistic regression model.

-   In the same figure, Panel B illustrates CP profiles for individual variables, age (continuous) and class (categorical).

![Source: Figure 10.1](img/10-cp-profiles/profile_age_class.png)

## Example: Titanic imputed dataset

Load packages

```{r 10-load-pckages}
suppressPackageStartupMessages({
  library(DALEX)
  library(rms)
  library(randomForest)
  })
```

Load `archivist` Titanic imputed dataset, logistic regression and randomg forest models, 'Henry' observation.

```{r 10-archivist}
titanic_imputed <- archivist::aread("pbiecek/models/27e5c")
titanic_lmr <- archivist::aread("pbiecek/models/58b24")
titanic_rf <- archivist::aread("pbiecek/models/4e0fc")
henry <- archivist::aread("pbiecek/models/a6538")
```

Let's build two explainers correpsonding to the logistic regresion and random forest models

```{r 10-explainers, warning=FALSE}
explain_lmr <- DALEX::explain(model = titanic_lmr, data = titanic_imputed[, -9],
    y = titanic_imputed$survived == "yes", label = "Logistic Regression", verbose = FALSE)

explain_lmr$model_info$type = "classification"

explain_rf <- DALEX::explain(model = titanic_rf,  data = titanic_imputed[, -9],
    y = titanic_imputed$survived == "yes", label = "Random Forest", verbose = FALSE)
```

Create a CP profiles with 'Henry' observation

```{r 10-cp-profiles, warning=FALSE}
cp_titanic_rf <- predict_profile(explainer = explain_rf, new_observation = henry)
cp_titanic_lmr <- predict_profile(explainer = explain_lmr, new_observation = henry)

ggplot2::theme_set(theme_ema())

cpplot_age_rf  <- plot(cp_titanic_rf, variables = "age") + 
  ggtitle("Ceteris Paribus for titanic_rf", "") + 
  scale_y_continuous("model response", limits = c(0,1))

cpplot_age_lmr <- plot(cp_titanic_lmr, variables = "age") + 
  ggtitle("Ceteris Paribus for titanic_lmr", "") + 
  scale_y_continuous("model response", limits = c(0,1))

cpplot_class_rf <- plot(cp_titanic_rf, variables = "class", variable_type = "categorical", categorical_type = "bars")  + 
  ggtitle("Ceteris Paribus for titanic_rf", "")

cpplot_class_lmr <- plot(cp_titanic_lmr, variables = "class", variable_type = "categorical", categorical_type = "bars") + 
  ggtitle("Ceteris Paribus for titanic_lmr", "")
```

```{r 10-cp-profiles-plot-1}
library(patchwork)

cpplot_age_lmr + cpplot_age_rf
```

Both CP profiles predict the survival probability for passenger Henry (1st class, age = 47, male), where the logistic regression results in 0.43 and the random forest model is 0.246.

```{r 10-cp-profiles-plot-2}
cpplot_class_lmr + cpplot_class_rf
```

Both models agree on the prediction direction, but not on the vector magnitude.

```{r 10-cp-profiles-plot-3}
plot(cp_titanic_rf) + 
  facet_wrap(~`_vname_`, ncol = 4, scales = "free_x") + 
  ggtitle("Ceteris Paribus for titanic_rf", "")
```

CP profiles for all continuous variables. What can we infer from the behavior of these variables?

## Pros and cons

Pros

-   Easy to understand and communicate visually (1D CP profile)
-   It is possible to show profiles for many variables or models in a single plot

Cons

-   Presence of correlated explanatory variables may lead to unrealistic and misleadings results
-   Not practical in case of a model with hundreds or thousands of variables

## Additional references

[Ceteris Paribus profiles](https://advanced-ds-in-r.netlify.app/posts/2021-03-24-imlglobal/#ceteris-paribus-profiles)

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