In a previous vignette, we introduced the “marginal effect” as a partial derivative. Since derivatives are only properly defined for continuous variables, we cannot use them to interpret the effects of changes in categorical variables. For this, we turn to *contrasts* between Adjusted predictions. In the context of this package, a “Contrast” is defined as:

The difference between two adjusted predictions, calculated for meaningfully different regressor values (e.g., College graduates vs. Others).

Consider a simple model with a logical and a factor variable:

```
library(marginaleffects)
tmp <- mtcars
tmp$am <- as.logical(tmp$am)
mod <- lm(mpg ~ am + factor(cyl), tmp)
```

The `marginaleffects`

function automatically computes contrasts for each level of the categorical variables, relative to the baseline category (`FALSE`

for logicals, and the reference level for factors), while holding all other values at their mode or mean:

```
mfx <- marginaleffects(mod)
summary(mfx)
#> Average marginal effects
#> Term Contrast Effect Std. Error z value Pr(>|z|) 2.5 % 97.5 %
#> 1 am TRUE - FALSE 2.560 1.298 1.973 0.04851 0.01675 5.103
#> 2 cyl 6 - 4 -6.156 1.536 -4.009 6.1077e-05 -9.16608 -3.146
#> 3 cyl 8 - 4 -10.068 1.452 -6.933 4.1147e-12 -12.91359 -7.222
#>
#> Model type: lm
#> Prediction type: response
```

The summary printed above says that moving from the reference category `4`

to the level `6`

on the `cyl`

factor variable is associated with a change of -6.156 in the adjusted prediction. Similarly, the contrast from `FALSE`

to `TRUE`

on the `am`

variable is equal to 2.560.

We can obtain the same results using the `emmeans`

package:

```
library(emmeans)
emm <- emmeans(mod, specs = "cyl")
contrast(emm, method = "revpairwise")
#> contrast estimate SE df t.ratio p.value
#> 6 - 4 -6.16 1.54 28 -4.009 0.0012
#> 8 - 4 -10.07 1.45 28 -6.933 <.0001
#> 8 - 6 -3.91 1.47 28 -2.660 0.0331
#>
#> Results are averaged over the levels of: am
#> P value adjustment: tukey method for comparing a family of 3 estimates
emm <- emmeans(mod, specs = "am")
contrast(emm, method = "revpairwise")
#> contrast estimate SE df t.ratio p.value
#> TRUE - FALSE 2.56 1.3 28 1.973 0.0585
#>
#> Results are averaged over the levels of: cyl
```

In models with multiplicative interactions, the contrasts of a categorical variable will depend on the values of the interacted variable:

We can now use the `newdata`

argument of the `marginaleffects`

function to compute contrasts for different values of the other regressors. As in the marginal effects vignette, the `datagrid`

function can be handy. Since we only care about the logical `am`

contrast, we use the `variables`

to indicate the subset of results to report:

```
marginaleffects(mod_int, newdata = datagrid(cyl = tmp$cyl), variables = "am")
#> rowid type term contrast dydx std.error am cyl
#> 1 1 response am TRUE - FALSE 1.441667 2.315925 FALSE 6
#> 2 2 response am TRUE - FALSE 5.175000 2.052848 FALSE 4
#> 3 3 response am TRUE - FALSE 0.350000 2.315925 FALSE 8
```

Once again, we obtain the same results with `emmeans`

:

```
emm <- emmeans(mod_int, specs = "am", by = "cyl")
contrast(emm, method = "revpairwise")
#> cyl = 4:
#> contrast estimate SE df t.ratio p.value
#> TRUE - FALSE 5.17 2.05 26 2.521 0.0182
#>
#> cyl = 6:
#> contrast estimate SE df t.ratio p.value
#> TRUE - FALSE 1.44 2.32 26 0.623 0.5390
#>
#> cyl = 8:
#> contrast estimate SE df t.ratio p.value
#> TRUE - FALSE 0.35 2.32 26 0.151 0.8810
```

As described above, the `marginaleffects`

package includes limited support to compute contrasts. Users who require more powerful features are encouraged to consider alternative packages such as emmeans, modelbased, or ggeffects. These packages offer useful features such as automatic back-transforms, p value correction for multiple comparisons, and more.