# Plotting interactions among categorical variables in regression models

#### Jacob Long

#### 2024-07-29

When trying to understand interactions between categorical predictors, the types of visualizations called for tend to differ from those for continuous predictors. For that (and some other) reasons, `interactions` offers support for these in `cat_plot` while continuous predictors (perhaps in interactions with categorical predictors) are dealt with in `interact_plot`, which has a separate vignette.

To be clear…

If all the predictors involved in the interaction are categorical, use `cat_plot`. You can also use `cat_plot` to explore the effect of a single categorical predictor.

If one or more are continuous, use `interact_plot`.

## Simple two-way interaction

First, let’s prep some data. I’m going to make some slight changes to the `mpg` dataset from `ggplot2` for didactic purposes to drop a few factor levels that have almost no values (e.g., there are 5 cylinder engines?).

    library(ggplot2)
    mpg2 <- mpg
    mpg2$cyl <- factor(mpg2$cyl)
    mpg2["auto"] <- "auto"
    mpg2$auto[mpg2$trans %in% c("manual(m5)", "manual(m6)")] <- "manual"
    mpg2$auto <- factor(mpg2$auto)
    mpg2["fwd"] <- "2wd"
    mpg2$fwd[mpg2$drv == "4"] <- "4wd"
    mpg2$fwd <- factor(mpg2$fwd)
    ## Drop the two cars with 5 cylinders (rest are 4, 6, or 8)
    mpg2 <- mpg2[mpg2$cyl != "5",]
    ## Fit the model
    fit3 <- lm(cty ~ cyl * fwd * auto, data = mpg2)

So basically what we’re looking at here is an interaction between number of cylinders in the engine of some cars and whether the car has all-wheel drive or two-wheel drive. The DV is fuel mileage in the city.

Here’s summary output for our model:

    library(jtools) # for summ()
    summ(fit3)

Observations | 230
Dependent variable | cty
Type | OLS linear regression

F(11,218) | 61.37
R² | 0.76
Adj. R² | 0.74

| Est. | S.E. | t val. | p
--- | --- | --- | --- | ---
(Intercept) | 21.37 | 0.39 | 54.19 | 0.00
cyl6 | -4.37 | 0.54 | -8.07 | 0.00
cyl8 | -8.37 | 0.67 | -12.51 | 0.00
fwd4wd | -2.91 | 0.76 | -3.83 | 0.00
automanual | 1.45 | 0.57 | 2.56 | 0.01
cyl6:fwd4wd | 0.59 | 0.96 | 0.62 | 0.54
cyl8:fwd4wd | 2.13 | 0.99 | 2.15 | 0.03
cyl6:automanual | -0.76 | 0.90 | -0.84 | 0.40
cyl8:automanual | 0.71 | 1.18 | 0.60 | 0.55
fwd4wd:automanual | -1.66 | 1.07 | -1.56 | 0.12
cyl6:fwd4wd:automanual | 1.29 | 1.52 | 0.85 | 0.40
cyl8:fwd4wd:automanual | -1.39 | 1.76 | -0.79 | 0.43
Standard errors: OLS

Let’s see what happens using all the default arguments:

    cat_plot(fit3, pred = cyl, modx = fwd)

This is with `geom = "point"`. We can see a main effect of `cyl` and maybe something is going on with the interaction as well, since the different between `2wd` and `4wd` seems to decrease as `cyl` gets higher.

You can also plot the observed data on the plot:

    cat_plot(fit3, pred = cyl, modx = fwd, plot.points = TRUE)

## Line plots

And since `cyl` does have a clear order, it might make more sense to connect those dots. Let’s try `geom = "line"`:

    cat_plot(fit3, pred = cyl, modx = fwd, geom = "line")

Okay, that makes the trend quite a bit clearer.

You have some other options, too. Suppose you will need this plot to look good in black and white. Let’s change the shape of those points for different values of the moderator.

    cat_plot(fit3, pred = cyl, modx = fwd, geom = "line", point.shape = TRUE)

You can change the line patterns as well for more clarity.

    cat_plot(fit3, pred = cyl, modx = fwd, geom = "line", point.shape = TRUE,
             vary.lty = TRUE)

You may also choose any color palette from `RColorBrewer` as well as several preset palettes available in `jtools`:

    cat_plot(fit3, pred = cyl, modx = fwd, geom = "line", point.shape = TRUE,
             colors = "Set2")

Use `?jtools_colors` for more on your color options.

## Bar/dynamite plots

Last but not least, you can also make bar charts, AKA dynamite plots. For many situations, these are not the best way to show your data, but I know it’s what a lot of people are looking for.

    cat_plot(fit3, pred = cyl, modx = fwd, geom = "bar")

The transparency of the fill color depends on the presence of the error bars and observed data points.

    cat_plot(fit3, pred = cyl, modx = fwd, geom = "bar", interval = FALSE)

Now let’s look with observed data:

    cat_plot(fit3, pred = cyl, modx = fwd, geom = "bar", interval = FALSE,
             plot.points = TRUE)