GRM Forests extend GRM Trees by creating ensembles of trees to provide more robust variable importance measures. 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).
To implement the tree-based GRM (GRMTree), you will install the following packages if not previously installed.
Once installed, load the packages as follows:
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)
#> Rows: 3,500
#> Columns: 17
#> $ MOS_Listen <chr> "5", "4", "5", "3", "5", "2", "5", "5", "2", "3", "3…
#> $ MOS_Info <chr> "5", "3", "5", "3", "5", "3", "5", "5", "2", "4", "3…
#> $ MOS_Advice_Crisis <chr> "5", "3", "5", "3", "5", "5", "5", "5", "4", "4", "3…
#> $ MOS_Confide <chr> "5", "4", "4", "2", "4", "4", "5", "5", "2", "3", "3…
#> $ MOS_Advice_Want <chr> "5", "2", "4", "3", "4", "3", "5", "5", "4", "3", "3…
#> $ MOS_Fears <chr> "5", "2", "5", "4", "5", "4", "5", "5", "1", "2", "1…
#> $ MOS_Personal <chr> "5", "2", "5", "1", "5", "2", "5", "5", "4", "2", "3…
#> $ MOS_Understand <chr> "5", "2", "5", "1", "4", "3", "5", "5", "4", "2", "3…
#> $ sex <chr> "Male", "Male", "Male", "Male", "Male", "Female", "M…
#> $ age <dbl> 69, 66, 72, 52, 61, 57, 61, 71, 77, 65, 55, 64, 45, …
#> $ residency <chr> "urban", "urban", "urban", "urban", "urban", "rural"…
#> $ depressed <chr> "No", "No", "No", "Yes", "No", "No", "Yes", "No", "N…
#> $ bmi <dbl> 22.85714, 33.59375, 24.38272, 31.14187, 25.88057, 24…
#> $ Education <chr> "Primary/High school", "College/University", "Colleg…
#> $ job <chr> "Unemployed", "Unemployed", "Unemployed", "Unemploye…
#> $ smoker <chr> "No", "No", "Yes", "No", "No", "No", "Yes", "Yes", "…
#> $ multimorbidity <chr> "2+", "2+", "1", "1", "2+", "2+", "2+", "1", "2+", "…
## 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)
## Explore the data
head(resp.data)
#> # A tibble: 6 × 17
#> MOS_Listen MOS_Info MOS_Advice_Crisis MOS_Confide MOS_Advice_Want MOS_Fears
#> <ord> <ord> <ord> <ord> <ord> <ord>
#> 1 5 5 5 5 5 5
#> 2 4 3 3 4 2 2
#> 3 5 5 5 4 4 5
#> 4 3 3 3 2 3 4
#> 5 5 5 5 4 4 5
#> 6 2 3 5 4 3 4
#> # ℹ 11 more variables: MOS_Personal <ord>, MOS_Understand <ord>, sex <fct>,
#> # age <dbl>, residency <fct>, depressed <fct>, bmi <dbl>, Education <fct>,
#> # job <fct>, smoker <fct>, multimorbidity <fct>
## Check the structure of the data
glimpse(resp.data)
#> Rows: 3,500
#> Columns: 17
#> $ MOS_Listen <ord> 5, 4, 5, 3, 5, 2, 5, 5, 2, 3, 3, 4, 5, 2, 5, 3, 5, 4…
#> $ MOS_Info <ord> 5, 3, 5, 3, 5, 3, 5, 5, 2, 4, 3, 4, 5, 2, 4, 4, 4, 3…
#> $ MOS_Advice_Crisis <ord> 5, 3, 5, 3, 5, 5, 5, 5, 4, 4, 3, 4, 2, 2, 4, 4, 4, 3…
#> $ MOS_Confide <ord> 5, 4, 4, 2, 4, 4, 5, 5, 2, 3, 3, 4, 5, 2, 5, 4, 5, 3…
#> $ MOS_Advice_Want <ord> 5, 2, 4, 3, 4, 3, 5, 5, 4, 3, 3, 4, 2, 2, 5, 4, 4, 2…
#> $ MOS_Fears <ord> 5, 2, 5, 4, 5, 4, 5, 5, 1, 2, 1, 4, 5, 2, 5, 4, 4, 4…
#> $ MOS_Personal <ord> 5, 2, 5, 1, 5, 2, 5, 5, 4, 2, 3, 4, 5, 2, 5, 4, 4, 3…
#> $ MOS_Understand <ord> 5, 2, 5, 1, 4, 3, 5, 5, 4, 2, 3, 4, 5, 2, 5, 4, 4, 3…
#> $ sex <fct> Male, Male, Male, Male, Male, Female, Male, Female, …
#> $ age <dbl> 69, 66, 72, 52, 61, 57, 61, 71, 77, 65, 55, 64, 45, …
#> $ residency <fct> urban, urban, urban, urban, urban, rural, urban, urb…
#> $ depressed <fct> No, No, No, Yes, No, No, Yes, No, No, No, Yes, No, N…
#> $ bmi <dbl> 22.85714, 33.59375, 24.38272, 31.14187, 25.88057, 24…
#> $ Education <fct> Primary/High school, College/University, College/Uni…
#> $ job <fct> Unemployed, Unemployed, Unemployed, Unemployed, Unem…
#> $ smoker <fct> No, No, Yes, No, No, No, Yes, Yes, No, No, No, Yes, …
#> $ multimorbidity <fct> 2+, 2+, 1, 1, 2+, 2+, 2+, 1, 2+, 2+, 2+, 2+, 1, 2+, …
## Create response as outcomes
resp.data$resp <- data.matrix(resp.data[, 1:8])## Get help on the control parameter
# ?grmforest.control
## GRMTree control parameters with Benjamini-Hochberg
grm_control <- grmtree.control(
minbucket = 350,
p_adjust = "BH", alpha = 0.05)
## Define the forest control parameters
forest_control <- grmforest.control(
n_tree = 3, # Number of trees (Reduced for vignette build time)
sampling = "bootstrap", # Bootstrap method; resampling also available
sample_fraction = 0.632,
mtry = sqrt(9), # Usually the square root of the number of covariates
control = grm_control,
remove_dead_trees = TRUE, # Remove any null GRMTree
seed = 123
)## Fit the GRM forest
mos_forest <- grmforest(
resp ~ sex + age + bmi + Education +
residency + depressed + job + multimorbidity + smoker,
data = resp.data,
control = forest_control
)
## Get the summary of the fitted forest
summary(mos_forest)
print(mos_forest)
## Plot a tree in the forest
plot(mos_forest$trees[[1]])## Calculate the variable importance
importance <- varimp(mos_forest, seed = 123, verbose = T)
## Print the result of the variable importance
print(importance)Example output:
age smoker bmi multimorbidity sex
403.07554 220.37908 39.02621 37.00120 32.06389
Education residency depressed job
0.00000 0.00000 0.00000 0.00000 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)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.