GRM Forests for Robust DIF Detection

In grmtree: Recursive Partitioning for Graded Response Models

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 7,
  fig.height = 5
)

Introduction

GRM Forests extend GRM Trees by creating ensembles of trees to provide more robust variable importance measures. The same forest works for longitudinal trees: see the Response Shift Detection with the Longitudinal GRMTree vignette for a longitudinal GRM Forest. This vignette covers:

• GRM Forest implementation

• Variable importance and variable importance plot.

See the vignette on getting started with grmtree package for a more detailed walkthrough of the tree-based graded response theory model (GRMTree).

Install and Load required packages

To implement the tree-based GRM (GRMTree), you will install the following packages if not previously installed.

## Install packages from CRAN repository
install.packages(c("dplyr", "grmtree"))

Once installed, load the packages as follows:

library(dplyr)        # For data manipulation
library(grmtree)      # For tree-based GRM DIF Test

Import and prepare the data

The data set used in this demonstration is a test/sample data for the package.

## Load the data
data("grmtree_data", package = "grmtree")

## Take a glimpse at the data
glimpse(grmtree_data)

## Prepare the data
resp.data <- grmtree_data %>% 
  mutate_at(vars(starts_with("MOS")), as.ordered) %>% 
  mutate_at(vars(c(sex, residency, depressed,
                   Education, job, smoker,
                   multimorbidity)), as.factor) 

## Note: Partitioning variables must be factor/numeric (character columns are coerced automatically, but converting yourself is cleaner).

## Explore the data
head(resp.data)

## Check the structure of the data
glimpse(resp.data)

## Create response as outcomes
resp.data$resp <- data.matrix(resp.data[, 1:8])

GRM Forests Implementation

Define the forest control parameters

## Get help on the control parameter
# ?grmforest.control

## GRMTree control parameters with Benjamini-Hochberg 
grm_control <- grmtree.control(
  minbucket = 350,
  p_adjust = "BH", alpha = 0.05)

## Define the forest control parameters
p <- 9

forest_control <- grmforest.control(
  n_tree = 3, # Number of trees (Reduced for vignette build time)
  sampling = "subsample",  # subsample method; bootstrap also available
  sample_fraction = 0.632,
  mtry = ceiling(sqrt(p)),  # Usually the square root of the number of covariates
  control = grm_control,
  remove_dead_trees = TRUE, # Remove any null GRMTree
  seed = 123,
  n_cores = 4            # Parallel now works (PSOCK/Windows included)
)

Grow the GRM Forest

## Fit the GRM forest
mos_forest <- grmforest(
  resp ~ sex + age + bmi + Education + 
  residency + depressed + job + multimorbidity + smoker,  
  data = resp.data,
  control = forest_control
)

## Get the summary of the fitted forest
print(mos_forest)

## Plot a tree in the forest
plot(mos_forest$trees[[1]])

Variable Importance

Compute the variable importance of each covariate

## Calculate the variable importance
importance <- varimp(mos_forest, seed = 123, verbose = T)

## Print the result of the variable importance
print(importance)

Example output:

GRM Forest variable importance (permutation)
  Trees: 50  Mean OOB log-likelihood: -9378.57 

       age         smoker    job     multimorbidity     sex      residency    bmi 
        12.391      6.646   1.904       1.855          1.594      0.687      0.137 
     depressed      Education 
         0.120         -0.262 

attr(,"n_tree")
[1] 50
attr(,"baseline")
[1] -9378.569

Plot the variable importance of each variable

Here plot.varimp creates a bar plot of variable importance scores with options for both ggplot2 and base R graphics.

## Plot the variable importance scores (ggplot is the default)
plot(importance)

## Plot onlt the top 5 importance variables
plot(importance, xlab = "", top_n = 5)

## Plot the base R version
plot(importance, use_ggplot = FALSE)

## Custom colors
plot(importance, col = c("green", "red"))

## Rename the variable names in the order from the variable importance result
names(importance) <- c("Age", "Smoking Status", "BMI",
                       "Multimorbidity", "Sex", "Education",
                       "Residency", "Depression", "Employment")

## Now create the plot with informative names
plot(importance)

Conclusion

GRM Forests provide more stable DIF detection by aggregating across many trees. Key advantages include robust variable importance measures, reduced overfitting, and better handling of complex interactions.

grmtree documentation built on Sept. 2, 2026, 1:07 a.m.