Computational Example: Mixed-Effects Logistic Regression (glmer)

Overview

This example uses the imv package with glmer() from lme4 to quantify how much item-level features improve prediction of verbal aggression responses, beyond what is explained by individual differences alone.

The data come from a study of verbal aggression (Vansteelandt, 2000), available as VerbAgg in the lme4 package. Participants were presented with frustrating scenarios and asked whether they would react in various verbally aggressive ways. The outcome is binary: did the person endorse the aggressive response (Y) or not (N)?

Because each person responds to multiple items, observations are clustered within individuals. A mixed-effects model with a random intercept for person accounts for this structure — some people are generally more aggressive than others regardless of the situation.

Setup

# install.packages("imv")
library(imv)
library(lme4)

data("VerbAgg", package = "lme4")

# Convert outcome to binary (0/1)
VerbAgg$y <- as.integer(VerbAgg$r2 == "Y")

# Preview
head(VerbAgg[, c("id", "item", "btype", "mode", "y")])

The key variables are:

  • y — binary outcome: 1 = verbally aggressive response endorsed
  • id — person identifier (the clustering variable; N = 316 persons)
  • btype — behavior type: curse, scold, or shout
  • mode — whether the item asks about wanting to respond (want) or actually doing so (do)

Fitting the Models

We compare two models:

  • Baseline (m0): random intercept for person only — captures individual differences in overall aggressiveness, but ignores all item-level features
  • Enhanced (m1): adds btype and mode as fixed effects — does knowing the type and mode of the aggressive behavior improve prediction beyond individual tendencies?
m0 <- glmer(y ~ 1 + (1 | id),
            data = VerbAgg, family = binomial)

m1 <- glmer(y ~ btype + mode + (1 | id),
            data = VerbAgg, family = binomial)

Computing the IMV

set.seed(42)
result <- imv(m0, m1, data = VerbAgg)
result

The imv() call recognizes the glmerMod class and dispatches to imv.glmerMod, which performs 4-fold cross-validation. In each fold, both models are refit on the training data and evaluated on the held-out fold. The allow.new.levels = TRUE argument is used internally so that persons appearing only in the test fold are handled gracefully.

Interpreting the Results

cat("Mean IMV:", round(result$mean, 3), "\n")
cat("SD:      ", round(result$sd,   3), "\n")
cat("95% CI:  [", round(result$ci["lower"], 3), ",",
                   round(result$ci["upper"], 3), "]\n")

A positive IMV indicates that btype and mode provide genuine predictive value beyond the random person effect alone. The IMV is expressed on the same scale as all other IMV comparisons: a value of, say, 0.05 means the enhanced model’s predictions would earn roughly 5 cents for every dollar staked under the baseline model’s odds.

Importantly, note that the baseline here is not the prevalence — it is a model that already accounts for clustering. The IMV thus measures the incremental value of the item-level fixed effects given the random structure, not relative to a flat prediction.

Going Further

The VerbAgg dataset also contains situ (situation type) and Anger (trait anger score) as additional predictors. You can assess their incremental value by extending m1:

m2 <- glmer(y ~ btype + mode + situ + Anger + (1 | id),
            data = VerbAgg, family = binomial)

set.seed(42)
result2 <- imv(m1, m2, data = VerbAgg)
result2

Here m1 is the baseline and m2 is the enhanced model — the IMV now measures whether adding situation type and trait anger improves prediction beyond behavior type and mode.