Plotting interaction effects in Bayesian models (using rstanarm)

Question

I'm trying to show how the effect of one variables changes with the values of another variable in a Bayesian linear model in rstanarm(). I am able to fit the model and take draws from the posterior to look at the estimates for each parameter, but it's not clear how to give some sort of plot of the effects of one variable in the interaction as the other changes and the associated uncertainty (i.e. a marginal effects plot). Below is my attempt:

library(rstanarm)

# Set Seed
set.seed(1)

# Generate fake data
w1 <- rbeta(n = 50, shape1 = 2, shape2 = 1.5)
w2 <- rbeta(n = 50, shape1 = 3, shape2 = 2.5)

dat <- data.frame(y = log(w1 / (1-w1)),
                  x = log(w2 / (1-w2)),
                  z = seq(1:50))

# Fit linear regression without an intercept:
m1 <- rstanarm::stan_glm(y ~ 0 + x*z, 
                         data = dat,
                         family = gaussian(),
                         algorithm = "sampling",
                         chains = 4,
                         seed = 123,
                         )


# Create data sets with low values and high values of one of the predictors
dat_lowx <- dat
dat_lowx$x <- 0

dat_highx <- dat
dat_highx$x <- 5

out_low <- rstanarm::posterior_predict(object = m1,
                                   newdata = dat_lowx)

out_high <- rstanarm::posterior_predict(object = m1,
                                        newdata = dat_highx)

# Calculate differences in posterior predictions
mfx <- out_high - out_low

# Somehow get the coefficients for the other predictor?

Answer 1

You could also use either the ggeffects-package, especially for marginal effects; or the sjPlot-package for marginal effects and other plot types (for marginal effects, sjPlot simply wraps the functions from ggeffects).

To plot marginal effects of interactions, use sjPlot::plot_model() with type = "int". Use mdrt.values to define which values to plot for continuous moderator variables, and use ppd to let prediction be based on either the posterior distribution of the linear predictor or draws from posterior predictive distribution.

library(sjPlot)
plot_model(m1, type = "int", terms = c("x", "z"), mdrt.values = "meansd")

plot_model(m1, type = "int", terms = c("x", "z"), mdrt.values = "meansd", ppd = TRUE)

or to plot marginal effects at other specific values, use type = "pred" and specify the values in the terms-argument:

plot_model(m1, type = "pred", terms = c("x", "z [10, 20, 30, 40]"))
# same as:
library(ggeffects)
dat <- ggpredict(m1, terms = c("x", "z [10, 20, 30, 40]"))
plot(dat)

There are more options, and also different ways of customizing the plot appearance. See related help files and package vignettes.