---
title: "Webinaire 1 — Le Quartet Causal"
subtitle: "Pourquoi corrélation ≠ causalité"
author: "Sosthène Akia · Stat4Research"
date: today
lang: fr
format:
  html:
    theme: cosmo
    toc: true
    embed-resources: true
    code-fold: false
execute:
  warning: false
  message: false
editor: source
---

# Configuration

```{r setup}
#| message: false
library(tidyverse)
library(ggdag)
library(patchwork)
library(broom)

set.seed(42)
n <- 1000
```

# Le Quartet Causal

## Dataset 1 : Causalité directe (X -> Y)

```{r}
quartet_1 <- tibble(
  X = rnorm(n),
  Y = 0.5 * X + rnorm(n, sd = 0.5)
)
```

## Dataset 2 : Confondant caché

```{r}
quartet_2 <- tibble(
  Z = rnorm(n),
  X = 0.7 * Z + rnorm(n, sd = 0.5),
  Y = 0.7 * Z + rnorm(n, sd = 0.5)
)
```

## Dataset 3 : Médiation

```{r}
quartet_3 <- tibble(
  X = rnorm(n),
  M = 0.6 * X + rnorm(n, sd = 0.4),
  Y = 0.7 * M + rnorm(n, sd = 0.5)
)
```

## Dataset 4 : Biais de collider

```{r}
quartet_4 <- tibble(
  X = rnorm(n),
  Y = rnorm(n),
  S = 0.5 * X + 0.5 * Y + rnorm(n, sd = 0.3)
) |> filter(S > median(S))
```

# Comparaison des corrélations

```{r}
bind_rows(
  quartet_1 |> summarise(cor_XY = cor(X, Y), dataset = "1. X -> Y"),
  quartet_2 |> summarise(cor_XY = cor(X, Y), dataset = "2. X <- Z -> Y"),
  quartet_3 |> summarise(cor_XY = cor(X, Y), dataset = "3. X -> M -> Y"),
  quartet_4 |> summarise(cor_XY = cor(X, Y), dataset = "4. Collider")
) |> mutate(cor_XY = round(cor_XY, 3))
```

# Régressions naïves

```{r}
bind_rows(
  tidy(lm(Y ~ X, data = quartet_1)) |> mutate(dataset = "1"),
  tidy(lm(Y ~ X, data = quartet_2)) |> mutate(dataset = "2"),
  tidy(lm(Y ~ X, data = quartet_3)) |> mutate(dataset = "3"),
  tidy(lm(Y ~ X, data = quartet_4)) |> mutate(dataset = "4")
) |> filter(term == "X")
```

# Visualisation des DAGs

```{r}
#| fig-height: 8

dag1 <- dagify(Y ~ X) |> tidy_dagitty() |> ggdag() + theme_dag()
dag2 <- dagify(Y ~ Z, X ~ Z) |> tidy_dagitty() |> ggdag() + theme_dag()
dag3 <- dagify(Y ~ M, M ~ X) |> tidy_dagitty() |> ggdag() + theme_dag()
dag4 <- dagify(S ~ X + Y) |> tidy_dagitty() |> ggdag() + theme_dag()

(dag1 + dag2) / (dag3 + dag4)
```

# Conclusion

L'inférence causale n'est pas optionnelle.
Le DAG est l'outil indispensable.

**Pour aller plus loin** : Cours S1 — stat4research.com

> Code 40% off cette semaine : `WEBINAR1`