---
title: "Contrasts and comparisons for generalized linear models"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Contrasts and comparisons for generalized linear models}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r set-options, echo = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  dev = "png",
  fig.width = 7,
  fig.height = 3.5,
  message = FALSE, warning = FALSE
)
options(width = 800)
arrow_color <- "#FF00cc"
p <- ht8 <- NULL

pkgs <- c("ggplot2", "see", "marginaleffects")

if (!all(vapply(pkgs, requireNamespace, quietly = TRUE, FUN.VALUE = logical(1L)))) {
  knitr::opts_chunk$set(eval = FALSE)
}
```


This vignette is the third in a 4-part series:

1. [**Contrasts and Pairwise Comparisons**](https://easystats.github.io/modelbased/articles/introduction_comparisons_1.html)

2. [**Comparisons of Slopes, Floodlight and Spotlight Analysis (Johnson-Neyman Intervals)**](https://easystats.github.io/modelbased/articles/introduction_comparisons_2.html)

3. **Contrasts and Comparisons for Generalized Linear Models**

4. [**Contrasts and Comparisons for Zero-Inflation Models**](https://easystats.github.io/modelbased/articles/introduction_comparisons_4.html)


# Contrasts and comparisons for GLM - logistic regression example

We will now show an example for non-Gaussian models. For GLM's (generalized linear models) with (non-Gaussian) link-functions, `estimate_means()` by default returns predicted values on the *response* scale. For example, predicted values for logistic regression models are shown as *probabilities*.

Let's look at a simple example.

```{r}
library(modelbased)
set.seed(1234)
dat <- data.frame(
  outcome = rbinom(n = 100, size = 1, prob = 0.35),
  x1 = as.factor(sample(1:3, size = 100, TRUE, prob = c(0.5, 0.2, 0.3))),
  x2 = rnorm(n = 100, mean = 10, sd = 7),
  x3 = as.factor(sample(1:4, size = 100, TRUE, prob = c(0.1, 0.4, 0.2, 0.3)))
)

m <- glm(outcome ~ x1 + x2 + x3, data = dat, family = binomial())
estimate_means(m, "x1")
```

## Contrasts and comparisons for categorical focal terms

Contrasts or comparisons - like predictions (see above) - are by default on the *response* scale, i.e. they're represented as difference between probabilities (in percentage points).

```{r message=TRUE}
estimate_contrasts(m, "x1")
```

```{r echo=FALSE}
p <- estimate_means(m, "x1")
ht8 <- estimate_contrasts(m, "x1")
```

The difference between the predicted probability of `x1 = 1` (21.2%) and `x1 = 2` (13.9%) is roughly 7.3 percentage points. This difference is not statistically significant (p = 0.417).

Contrasts or comparisons can also be represented on the link-scale, in this case as _log-odds_. To do so, use `predict = "link"`.

```{r message=TRUE}
estimate_contrasts(m, "x1", predict = "link")
```

The `transform` argument in `estimate_contrasts()` can be used transform comparisons. For example, to transform contrasts to _odds ratios_, we can use `transform = exp` in combination with `predict = "link"`.

```{r message=TRUE}
estimate_contrasts(m, "x1", predict = "link", transform = exp)
```

[Go to next vignette: **Contrasts and Comparisons for Zero-Inflation Models**](https://easystats.github.io/modelbased/articles/introduction_comparisons_4.html)