Title:	Recursive Partitioning for Graded Response Models
Version:	0.1.0
Date:	2026-01-08
Maintainer:	Olayinka I. Arimoro <olayinka.arimoro@ucalgary.ca>
Description:	Provides methods for recursive partitioning based on the 'Graded Response Model' ('GRM'), extending the 'MOB' algorithm from the 'partykit' package. The package allows for fitting 'GRM' trees that partition the population into homogeneous subgroups based on item response patterns and covariates. Includes specialized plotting functions for visualizing 'GRM' trees with different terminal node displays (threshold regions, parameter profiles, and factor score distributions). For more details on the methods, see Samejima (1969) <doi:10.1002/J.2333-8504.1968.TB00153.X>, Komboz et al. (2018) <doi:10.1177/0013164416664394> and Arimoro et al. (2025) <doi:10.1007/s11136-025-04018-6>.
License:	GPL-3
Depends:	R (≥ 4.1.0), partykit (≥ 1.2-9), mirt (≥ 1.36.1)
Imports:	stats, graphics, grid, dplyr, ggplot2, rlang, magrittr, strucchange
Suggests:	hlt, testthat (≥ 3.0.0), knitr, rmarkdown, psychotools, psychotree, psych
Config/testthat/edition:	3
Encoding:	UTF-8
RoxygenNote:	7.3.3
URL:	https://github.com/Predicare1/grmtree
BugReports:	https://github.com/Predicare1/grmtree/issues
Repository:	CRAN
VignetteBuilder:	knitr
LazyData:	true
NeedsCompilation:	no
Packaged:	2026-01-09 19:57:34 UTC; Olayinka A
Author:	Olayinka I. Arimoro [aut, cre], Tolulope T. Sajobi [aut], Lisa M. Lix [aut], Matthew T. James [ctb], Maria Santana [ctb], Emmanuel Ugochukwu [ctb]
Date/Publication:	2026-01-14 18:00:02 UTC

Internal Function: Apply Function to Models in Nodes

Description

Applies a function to the GRM models in specified nodes of a tree. This is an internal helper function and not meant to be called directly.

Usage

apply_to_models(object, node = NULL, FUN = NULL, drop = FALSE, ...)

Arguments

Value

List of results (or single result if drop=TRUE and length(node)=1).

Extract Discrimination Parameters from GRM Tree

Description

Extracts discrimination parameters (slope parameters) for each item from all terminal nodes of a graded response model tree. The discrimination parameter indicates how well an item distinguishes between respondents with different levels of the latent trait.

Usage

discrpar_grmtree(object, node = NULL, ...)

Arguments

Value

A data.frame with discrimination parameters for each item in each node, with columns:

See Also

grmtree fits a Graded Response Model Tree, grmforest for GRM Forests, fscores_grmtree for computing factor scores, threshpar_grmtree for extracting threshold parameters, itempar_grmtree for extracting item parameters

Examples

  library(grmtree)
  library(hlt)
  data("asti", package = "hlt")
  asti$resp <- data.matrix(asti[, 1:4])

  # Fit GRM tree with gender and group as partitioning variables
  tree <- grmtree(resp ~ gender + group,
          data = asti,
          control = grmtree.control(minbucket = 30))

  # Get all discrimination parameters
  discr <- discrpar_grmtree(tree)
  print(discr)

Compute Latent Factor Scores for Each Terminal Node in a GRM Tree

Description

This function calculates latent factor scores for each terminal node in a GRM tree object using specified scoring method (EAP, MAP, ML, or WLE).

Usage

fscores_grmtree(grmtree_obj, method = "EAP")

Arguments

Value

A named list where each element contains the factor scores for a terminal node. Names correspond to node IDs. Returns NULL for nodes where computation fails. If no scores can be computed for any node, returns NULL with a warning.

See Also

fscores for factor scoring methods, grmtree fits a Graded Response Model Tree, grmforest for GRM Forests, threshpar_grmtree for extracting threshold parameters, discrpar_grmtree for extracting discrimination parameters, itempar_grmtree for extracting item parameters, generate_node_scores_dataset generates combined dataset with node assignments and factor scores

Examples

  library(grmtree)
  library(hlt)
  data("asti", package = "hlt")
  asti$resp <- data.matrix(asti[, 1:4])

  # Fit GRM tree with gender and group as partitioning variables
  tree <- grmtree(resp ~ gender + group,
          data = asti,
          control = grmtree.control(minbucket = 30))

# Compute EAP scores for all terminal nodes
node_scores <- fscores_grmtree(tree)

# Compute MAP scores instead
node_scores_map <- fscores_grmtree(tree, method = "MAP")

Generate Combined Dataset with Node Assignments and Factor Scores

Description

Creates a dataset combining original data with node assignments and computed factor scores. Maintains original row order while adding node membership and factor score information.

Usage

generate_node_scores_dataset(grmtree_obj, method = "EAP")

Arguments

Value

A data.frame containing: - Original variables from the model frame - 'node': Factor indicating terminal node membership (e.g., "Node 1") - 'factor_score': Computed latent factor scores Rows are in original order with sequential row names.

See Also

grmtree fits a Graded Response Model Tree, grmforest for GRM Forests, fscores_grmtree for computing factor scores, threshpar_grmtree for extracting threshold parameters, discrpar_grmtree for extracting discrimination parameters, itempar_grmtree for extracting item parameters

Examples

  library(grmtree)
  library(hlt)
  data("asti", package = "hlt")
  asti$resp <- data.matrix(asti[, 1:4])

  # Fit GRM tree with gender and group as partitioning variables
  tree <- grmtree(resp ~ gender + group,
          data = asti,
          control = grmtree.control(minbucket = 30))

# Generate combined dataset
scored_data <- generate_node_scores_dataset(tree)

# Plot scores by node
boxplot(factor_score ~ node, data = scored_data)

Internal Function: Fit Graded Response Model

Description

Fits a graded response model (GRM) to item response data. This is an internal function called by grmtree and is not intended to be used directly.

Usage

grmfit(
  y,
  x = NULL,
  start = NULL,
  weights = NULL,
  offset = NULL,
  ...,
  estfun = FALSE,
  object = FALSE
)

Arguments

Value

A list containing:

Fit a Forest of Graded Response Model Trees for Ensemble-Based DIF Detection

Description

This function implements a forest of graded response model trees (GRM Forest) using bootstrap aggregation (bagging) or random subsampling to enhance the detection and analysis of differential item functioning (DIF) in polytomous items. The GRM Forest approach combines the strengths of multiple GRMTrees to provide more robust and stable DIF detection, particularly for complex datasets with high-dimensional covariates or subtle DIF patterns.

Usage

grmforest(formula, data, control = grmforest.control(), ...)

Arguments

Details

The algorithm works by fitting multiple GRMTrees, each on a random sample of the original data (either through bootstrap sampling or subsampling). For each tree, approximately one-third of the observations are left out as out-of-bag (OOB) samples, which are used for internal validation and variable importance calculation. The ensemble approach reduces variance, minimizes overfitting, and provides more reliable identification of covariates associated with DIF.

Key advantages of the GRM Forest approach include:

• Enhanced stability in DIF detection across different sampling variations

• Robust variable importance measures that quantify the relative contribution of each covariate to DIF patterns

• Reduced false positive rates through consensus-based detection

• Ability to handle high-dimensional covariate spaces effectively

• Internal validation through out-of-bag error estimation

The forest implementation supports both bootstrap aggregation (where samples are drawn with replacement) and subsampling (without replacement), allowing flexibility for different data characteristics and research objectives.

Value

An object of class grmforest containing:

See Also

grmtree fits a Graded Response Model Tree, grmtree.control creates a control object for grmtree, grmforest.control creates a control object for grmforest, varimp calculates the variable importance for GRM Forest, plot.varimp creates a bar plot of variable importance scores

Examples

  library(grmtree)
  library(hlt)
  data("asti", package = "hlt")
  asti$resp <- data.matrix(asti[, 1:4])

  # Fit forest with default parameters
  forest <- grmforest(resp ~ gender + group, data = asti)

  # Fit with custom control
  ctrl <- grmforest.control(n_tree = 50, sampling = "subsample")
  forest <- grmforest(resp ~ gender + group, data = asti, control = ctrl)

Control Parameters for GRM Forest

Description

Creates a control object for grmforest containing parameters that control the forest growing process including sampling, tree growing, and error handling.

Usage

grmforest.control(
  n_tree = 100,
  sampling = "bootstrap",
  sample_fraction = 0.632,
  mtry = NULL,
  remove_dead_trees = TRUE,
  control = grmtree.control(),
  alpha = 0.05,
  minbucket = 20,
  seed = NULL
)

Arguments

Value

A list of class grmforest_control containing:

See Also

grmtree.control creates a control object for grmtree, plot.grmtree creates plot for the grmtree object, grmforest for GRM Forests,

Examples

library(grmtree)
# Control with 50 trees using subsampling
ctrl <- grmforest.control(n_tree = 50, sampling = "subsample")

# Control with specific tree parameters
ctrl <- grmforest.control(
  control = grmtree.control(minbucket = 30, alpha = 0.01)
)

Fit a Graded Response Model Tree for Differential Item Functioning Detection

Description

This function implements a tree-based graded response model (GRM) using model-based recursive partitioning to detect and account for differential item functioning (DIF) in polytomous items. The GRMTree combines the statistical framework of item response theory with recursive partitioning to identify heterogeneous subgroups in the population where item parameters (discrimination and thresholds) vary systematically across covariates.

Usage

grmtree(
  formula,
  data,
  na.action = na.omit,
  control = grmtree.control(),
  mtry = NULL,
  ...
)

Arguments

Details

The algorithm works by first estimating a global GRM for the entire sample, then recursively testing for parameter instability with respect to available covariates. When significant DIF is detected, the sample is partitioned into homogeneous subgroups, each with their own set of item parameters. This approach allows for the identification of complex interaction effects and provides interpretable tree structures that visualize how item functioning varies across different patient subgroups.

GRMTree is particularly useful in health outcomes research where patient-reported outcome measures may function differently across diverse demographic, clinical, or socioeconomic subgroups. The resulting tree diagrams facilitate the development of personalized assessment strategies and can inform targeted interventions by identifying specific patient characteristics associated with differential item interpretation.

Conventional Graded Response Model (GRM)

Let Y_{im} denote the response of the i^{th} (i=1,\ldots,N) individual to the m^{th} (m = 1,2,\ldots,M) item. The graded response model is described as:

P(Y_{im} \geq j | \tau_{mj}, \lambda_m, \theta_i) = \frac{\exp(-(\tau_{mj} - \lambda_m \theta_i))}{1 + \exp(-(\tau_{mj} - \lambda_m \theta_i))}

where:

• P(Y_{im} \geq j | \tau_{mj}, \lambda_m, \theta_i) is the probability that individual i's response is in category j or higher on item m,

• \tau_{mj} is the threshold parameter between categories j-1 and j for item m,

• \lambda_m is the discrimination parameter for item m,

• \theta_i \sim N(0,1) is the latent trait score for individual i.

This parametrization is equivalent to the conventional IRT formulation where item discrimination is a_m = \lambda_m and item difficulty is b_{mj} = \tau_{mj} / \lambda_m.

Graded Response Model Tree (GRMTree) Implementation

The GRMTree is a hybrid model that integrates the GRM with model-based recursive partitioning to detect and account for differential item functioning (DIF) across subgroups defined by covariates. The algorithm proceeds through the following steps:

Step 1: Global Model Estimation

Estimate the GRM item parameters (\hat{\tau}_{mj}, \hat{\lambda}_m) jointly for all individuals in the study cohort at the root node via maximum likelihood estimation:

\hat{\beta}_{\text{global}} = \arg\max_{\beta} \sum_{i=1}^N \log L(\beta; \mathbf{y}_i)

where \beta = (a_1, \ldots, a_J, b_{11}, \ldots, b_{J,m-1}) contains all item parameters (discrimination and difficulty), providing a baseline model assuming parameter invariance.

Step 2: Parameter Stability Testing

For each available covariate X_p (p = 1, \ldots, P), assess the stability of the item parameters by conducting score-based structural change tests. This involves: 1. Calculating the score function contributions s(\hat{\beta}; y_i, x_i) for each individual, 2. Ordering these scores with respect to each covariate X_p, 3. Testing the null hypothesis H_0: \mathbb{E}[s(\hat{\beta}; y_i, x_i)] = 0 for all i against the alternative that scores fluctuate systematically with X_p, indicating parameter instability (DIF).

Step 3: Recursive Partitioning

If significant instability is detected (p < \alpha_{\text{adj}}):

• Covariate Selection: Identify the covariate X_p^* with the most significant instability (smallest adjusted p-value),

• Split Point Determination: Find the optimal cut-point c^* that maximizes the partitioned log-likelihood:

  \ell_{\text{left}}(\beta) + \ell_{\text{right}}(\beta) = \sum_{i: X_{pi} \leq c^*} \log L(\beta; y_i) + \sum_{i: X_{pi} > c^*} \log L(\beta; y_i)

  over all possible cut-points on X_p^*,

• Sample Splitting: Partition the sample into two child nodes based on the rule X_p^* \leq c^*.

Step 4: Recursive Application & Stopping Criteria

Repeat Steps 1-3 recursively within each resulting child node until one of the following stopping criteria is met:

1. No Significant Instability: No covariate shows significant parameter instability after multiple testing correction (\alpha_{\text{adj}} = \alpha/m, where multiple adjustment methods can be applied, including Bonferroni, Holm, Benjamini-Hochberg, etc.).

2. Minimum Node Size: The subsample size falls below a prespecified minimum (e.g., n < 10 \times the number of item parameters).

Formal GRMTree Structure

The final GRMTree provides a piecewise GRM where each terminal node represents a subgroup with homogeneous item parameters, explicitly modeling the detected DIF structure within the data. The resulting GRMTree model can be expressed as a mixture of subgroup-specific GRMs:

P(Y_{ij} = k | \theta_i, \mathbf{x}_i) = \sum_{b=1}^B I(\mathbf{x}_i \in \mathcal{X}_b) \cdot P_b(Y_{ij} = k | \theta_i)

where:

• B is the number of terminal nodes,

• \mathcal{X}_b is the covariate subspace defining terminal node b,

• P_b is the node-specific GRM with parameters \beta_b,

• I(\cdot) is the indicator function.

Each terminal node b contains a complete GRM with:

• Node-specific item parameters: \beta_b = (a_{1b}, \ldots, a_{Jb}, b_{11b}, \ldots, b_{J,m-1,b})

• Local ability distribution: \theta_i | \mathbf{x}_i \in \mathcal{X}_b \sim N(0, 1)

This approach allows differential item functioning (DIF) to be detected and modeled explicitly through the tree structure, where item parameters can vary across subgroups defined by covariates, while maintaining the conditional distribution of the latent trait within each subgroup.

Post-Hoc Multiple Comparison Adjustments

For holm, BH, BY, hochberg, and hommel methods, the algorithm employs a two-stage approach: (1) build a tree using initial_alpha as the splitting threshold, (2) apply global p-value adjustment across all splits, and (3) prune splits that do not meet the adjusted threshold alpha. This differs from Bonferroni correction, which is applied locally during tree construction via partykit::mob. The choice of initial_alpha represents a statistical trade-off. The default (min(3 * alpha, 0.20)) provides a balance between power and computational efficiency. Note that global post-hoc adjustments in hierarchical tree structures may be conservative compared to per-node adjustments, as they account for all tests performed during tree exploration. This global adjustment approach controls the tree-wide error rate and may be conservative (Type I error often <3%). This conservativeness ensures strong control of family-wise error rate or false discovery rate across all splits in the tree. Users requiring less conservative control may prefer the Bonferroni method, which applies per-node adjustment during tree construction.

Value

An object of class grmtree inheriting from modelparty containing the fitted tree structure.

Author(s)

Olayinka Imisioluwa Arimoro olayinka.arimoro@ucalgary.ca, Lisa M. Lix, Tolulope T. Sajobi

References

Methodological Foundations

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph Supplement, 34, 100-114.

Strobl, C., Kopf, J., & Zeileis, A. (2015). Rasch trees: A new method for detecting differential item functioning in the Rasch model. Psychometrika, 80(2), 289-316.

Komboz, B., Strobl, C., & Zeileis, A. (2018). Tree-based global model tests for polytomous Rasch models. Educational and psychological measurement, 78(1), 128-166. https://doi.org/10.1177/0013164416664394

Arimoro, O. I., Lix, L. M., Patten, S. B., Sawatzky, R., Sebille, V., Liu, J., Wiebe, S., Josephson, C. B., & Sajobi, T. T. (2025). Tree-based latent variable model for assessing differential item functioning in patient-reported outcome measures: a simulation study. Quality of Life Research. https://doi.org/10.1007/s11136-025-04018-6

Applied Examples

Arimoro, O. I., Josephson, C. B., James, M. T., Patten, S. B., Wiebe, S., Lix, L. M., & Sajobi, T. T. (2024). Screening for depression in patients with epilepsy: same questions but different meaning to different patients. Quality of Life Research, 33(12), 3409-3419. https://doi.org/10.1007/s11136-024-03782-1

See Also

print.grmtree prints the detailed summary results of the grmtree object, grmtree.control creates a control object for grmtree, plot.grmtree creates plot for the grmtree object, grmforest for GRM Forests, varimp calculates the variable importance for GRM Forest, fscores_grmtree for computing factor scores, threshpar_grmtree for extracting threshold parameters, discrpar_grmtree for extracting discrimination parameters, itempar_grmtree for extracting item parameters

Examples

  library(grmtree)
  library(hlt)

  # Prepare the asti data (from the hlt package)
  data("asti", package = "hlt")
  asti$resp <- data.matrix(asti[, 1:4])

  # Fit GRM tree with gender and group as partitioning variables
  tree <- grmtree(resp ~ gender + group,
          data = asti,
          control = grmtree.control(minbucket = 30))

  ## Print and plot the tree
  print(tree)
  plot(tree)

  # Extract item parameters for specific subgroups
  discr_params <- discrpar_grmtree(tree)
  threshold_params <- threshpar_grmtree(tree)

Control Parameters for GRM Trees

Description

Creates a control object for grmtree containing various parameters that control the tree growing process.

Usage

grmtree.control(
  minbucket = 20,
  p_adjust = "none",
  alpha = 0.05,
  initial_alpha = NULL,
  ...
)

Arguments

Value

A list of control parameters with class grmtree_control.

See Also

grmtree fits a Graded Response Model Tree

Examples

# Use Bonferroni correction with alpha = 0.01
ctrl <- grmtree.control(p_adjust = "bonferroni", alpha = 0.01)

Medical Outcomes Study Social Support Survey (MOS-SS) Test Data

Description

A dataset containing sample responses to the MOS-SS emotional domain items and demographic variables. This data is provided for testing and demonstration purposes within the grmtree package. The items are numbered 1-5, representing None of the time, A little of the time, Some of the time, Most of the time, All of the time, respectively.

Usage

grmtree_data

Format

A tibble with 3,500 rows and 17 variables:

MOS_Listen

Someone you can count on to listen to you when you need to talk (1-5 Likert scale)

MOS_Info

Someone to give you information to help you understand a situation (1-5 Likert scale)

MOS_Advice_Crisis

Someone to give good advice about a crisis (1-5 Likert scale)

MOS_Confide

Someone to confide in or talk to about yourself or your problems (1-5 Likert scale)

MOS_Advice_Want

Someone whose advice you really want (1-5 Likert scale)

MOS_Fears

Someone to share private worries or fears (1-5 Likert scale)

MOS_Personal

Someone to turn to for suggestions about how to deal with a personal problem (1-5 Likert scale)

MOS_Understand

Someone who understands your problems (1-5 Likert scale)

sex

Gender (Male, Female)

age

Age in years (numeric)

residency

Residence location (rural, urban)

depressed

Depression status (No, Yes)

bmi

Body Mass Index (numeric)

Education

Education level (Primary/High school, College/University)

job

Employment status (Employed, Unemployed)

smoker

Smoking status (No, Yes)

multimorbidity

Number of chronic conditions (0, 1, 2+)

Source

Simulated data generated for package testing and demonstration

Examples

  library(dplyr)

  # Load and take a glimpse at the data
  data(grmtree_data, package = "grmtree")
  glimpse(grmtree_data)

Extract Item Parameters from GRM Tree

Description

Extracts both discrimination parameters and average threshold parameters for each item from all terminal nodes of a graded response model tree. This provides a comprehensive view of item characteristics across different nodes of the tree.

Usage

itempar_grmtree(object, node = NULL, ...)

Arguments

Value

A data.frame with item parameters for each item in each node, with columns:

See Also

grmtree fits a Graded Response Model Tree, grmforest for GRM Forests, fscores_grmtree for computing factor scores, threshpar_grmtree for extracting threshold parameters, discrpar_grmtree for extracting discrimination parameters

Examples

  library(grmtree)
  library(hlt)
  data("asti", package = "hlt")
  asti$resp <- data.matrix(asti[, 1:4])

  # Fit GRM tree with gender and group as partitioning variables
  tree <- grmtree(resp ~ gender + group,
          data = asti,
          control = grmtree.control(minbucket = 30))

  # Get all item parameters
  items <- itempar_grmtree(tree)
  print(items)

Plot Method for GRM Tree Objects

Description

Visualizes a GRM (Graded Response Model) tree with different types of terminal node plots. This function extends plot.modelparty from the partykit package with specialized visualizations for GRM trees.

Usage

## S3 method for class 'grmtree'
plot(
  x,
  type = c("regions", "profile", "histogram"),
  what = c("item", "threshold", "discrimination"),
  tnex = 2L,
  drop_terminal = TRUE,
  spacing = 0.1,
  ...
)

Arguments

Details

The function provides three visualization types:

• Regions plot: Shows threshold parameters as colored regions, useful for visualizing the difficulty parameters across items and nodes.

• Profile plot: Displays either item parameters (discrimination and average thresholds), just thresholds, or just discrimination parameters as line plots across items.

• Histogram: Shows the distribution of factor scores in each node with an overlaid normal curve.

Value

Invisibly returns the GRM tree object. Primarily called for its side effect of producing a plot.

See Also

plot.modelparty for the underlying plotting infrastructure, grmtree for creating GRM tree objects, plot.varimp creates a bar plot of variable importance scores

Examples

library(grmtree)
library(hlt)
data("asti", package = "hlt")
asti$resp <- data.matrix(asti[, 1:4])

# Fit GRM tree with gender and group as partitioning variables
tree <- grmtree(resp ~ gender + group,
          data = asti,
          control = grmtree.control(minbucket = 30))

# Default regions plot
plot(tree)

# Profile plot showing item parameters
plot(tree, type = "profile")

# Profile plot showing only thresholds
plot(tree, type = "profile", what = "threshold")

# Histograms of factor scores
plot(tree, type = "histogram")

Plot Variable Importance

Description

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

Usage

## S3 method for class 'varimp'
plot(x, top_n = NULL, use_ggplot = TRUE, ...)

Arguments

Value

Invisibly returns the input object.

See Also

varimp calculates the variable importance for GRM Forest, grmforest for GRM Forests, grmforest.control creates a control object for grmforest, plot.grmtree creates plot for the grmtree object

Examples

 library(grmtree)
 library(hlt)
 data("asti", package = "hlt")
 asti$resp <- data.matrix(asti[, 1:4])

 # Fit forest with default parameters
 forest <- grmforest(resp ~ gender + group, data = asti)
 imp <- varimp(forest)
 plot(imp)
 plot(imp, top_n = 1) ## select top 1 importance variable
 plot(imp, use_ggplot = FALSE) # Use base R graphics

Print Method for GRM Forest

Description

Print Method for GRM Forest

Usage

## S3 method for class 'grmforest'
print(x, ...)

Arguments

Value

Invisibly returns the input object

Print Method for GRM Tree Objects

Description

Displays a formatted summary of a GRM (Graded Response Model) tree object. This function extends print.modelparty from the partykit package with specialized formatting for GRM trees.

Usage

## S3 method for class 'grmtree'
print(
  x,
  title = "Graded Response Model Tree",
  objfun = "negative log-likelihood",
  ...
)

Arguments

Details

The print method provides a comprehensive summary of the GRM tree, including:

• Model formula used for fitting

• Tree structure with node information

• Item parameter estimates for each terminal node

• Confidence intervals for parameters

• Group parameters (mean and covariance)

• Summary statistics (number of nodes, objective function value)

Value

Invisibly returns the GRM tree object. Primarily called for its side effect of printing a formatted summary.

See Also

print.modelparty for the underlying printing infrastructure, grmtree for creating GRM tree objects

Examples

library(grmtree)
library(hlt)
data("asti", package = "hlt")
asti$resp <- data.matrix(asti[, 1:4])

# Fit GRM tree
tree <- grmtree(resp ~ gender + group,
                data = asti,
                control = grmtree.control(minbucket = 30))

# Print the tree summary
print(tree)

# Alternative syntax (automatically calls print.grmtree)
tree

Extract Threshold Parameters from GRM Tree

Description

Extracts threshold parameters for each item from all terminal nodes of a graded response model tree. The thresholds represent the points on the latent trait continuum where the probability of scoring in adjacent response categories is equal.

Usage

threshpar_grmtree(object, node = NULL, ...)

Arguments

Value

A data.frame with threshold parameters for each item in each node, with columns:

See Also

grmtree fits a Graded Response Model Tree, grmforest for GRM Forests, fscores_grmtree for computing factor scores, discrpar_grmtree for extracting discrimination parameters, itempar_grmtree for extracting item parameters

Examples

  library(grmtree)
  library(hlt)

  data("asti", package = "hlt")
  asti$resp <- data.matrix(asti[, 1:4])

  # Fit GRM tree with gender and group as partitioning variables
  tree <- grmtree(resp ~ gender + group,
          data = asti,
          control = grmtree.control(minbucket = 30))

  # Get all thresholds
  thresholds <- threshpar_grmtree(tree)
  print(thresholds)

Calculate Variable Importance for GRM Forest

Description

Computes permutation importance scores for variables in a GRM forest using out-of-bag samples. Importance is measured by the decrease in log-likelihood when a variable's values are permuted.

Usage

varimp(forest, method = "permutation", verbose = FALSE, seed = NULL)

Arguments

Value

A named numeric vector of importance scores with class varimp. Higher values indicate more important variables.

See Also

grmtree fits a Graded Response Model Tree, grmforest for GRM Forests, grmforest.control creates a control object for grmforest, plot.varimp creates a bar plot of variable importance scores

Examples

library(grmtree)
library(hlt)
data("asti", package = "hlt")
asti$resp <- data.matrix(asti[, 1:4])

## Fit the GRM Forest
forest <- grmforest(resp ~ gender + group, data = asti,
control = grmforest.control(n_tree = 5))
  importance <- varimp(forest)

## Print and plot the variable importance scores
print(importance)
plot(importance)