Example Dataset for DIFtree

Description

A dataset used for demonstrating the IFTPredictor package. This dataset includes response data (columns 1-20) and covariate data (columns 21-24)

Usage

mydata

Format

A data frame with 500 rows and 24 variables:

V1

Binary response variable (numeric: 0 or 1) representing item 1.

V2

Binary response variable (numeric: 0 or 1) representing item 2.

V3

Binary response variable (numeric: 0 or 1) representing item 3.

V4

Binary response variable (numeric: 0 or 1) representing item 4.

V5

Binary response variable (numeric: 0 or 1) representing item 5.

V6

Binary response variable (numeric: 0 or 1) representing item 6.

V7

Binary response variable (numeric: 0 or 1) representing item 7.

V8

Binary response variable (numeric: 0 or 1) representing item 8.

V9

Binary response variable (numeric: 0 or 1) representing item 9.

V10

Binary response variable (numeric: 0 or 1) representing item 10.

V11

Binary response variable (numeric: 0 or 1) representing item 11.

V12

Binary response variable (numeric: 0 or 1) representing item 12.

V13

Binary response variable (numeric: 0 or 1) representing item 13.

V14

Binary response variable (numeric: 0 or 1) representing item 14.

V15

Binary response variable (numeric: 0 or 1) representing item 15.

V16

Binary response variable (numeric: 0 or 1) representing item 16.

V17

Binary response variable (numeric: 0 or 1) representing item 17.

V18

Binary response variable (numeric: 0 or 1) representing item 18.

V19

Binary response variable (numeric: 0 or 1) representing item 19.

V20

Binary response variable (numeric: 0 or 1) representing item 20.

x1

An integer variable (e.g., a grouping factor or categorical covariate).

x2

A continuous numeric covariate.

x3

An integer variable (binary: 0 or 1).

x4

A continuous numeric covariate.

Examples

data("mydata", package = "IFTPredictor")
head(mydata)

Predictions Using Item-Focused Tree Models

Description

This function predicts item response probabilities and item responses using the item-focused tree (IFT) model. The item-focused tree model combines logistic regression with recursive partitioning to detect Differential Item Functioning (DIF) in dichotomous items. The model applies partitioning rules to the data, splitting it into homogeneous subgroups, and uses logistic regression within each subgroup to explain the data. Differential Item Functioning detection is achieved by examining potential group differences in item response patterns. This model produces tree diagrams to visualize homogeneous subgroups within the population exhibiting similar response patterns and may therefore be helpful for developing personalized interventions and optimizing resource allocation in healthcare.

Usage

predict_item_responses(model, dataset, total_score)

Arguments

Details

The logistic regression model for the i-th PROM item is defined as:

\log \left( \frac{P(Y_{pi} = 1 \mid S_{p}, g)}{P(Y_{pi} = 0 \mid S_{p}, g)} \right) = \eta_{pi} = \beta_{0i} + S_{p} \beta_{i} + \gamma_{ig},

where, Y_{pi} \in \{0, 1\}: The response of person p to the i-th item. p = 1, 2, \dots, P: The number of persons. i = 1, 2, \dots, I: The number of items. g: Group membership (g = 0 for the reference group, g = 1 for the focal group). S_p: The ability level (e.g., total PROM score) of person p. \beta_{0i}: The intercept or item difficulty parameter. \beta_{i}: The slope or item discrimination parameter. \gamma_{ig}: The group-specific parameter.

The IFT model extends this logistic regression model for DIF detection for the i-th PROM item:

\eta_{pi} = \beta_i S_p + \left[ \gamma_{ik} I(x_{pl} \leq c_l) + \gamma_{ir} I(x_{pl} > c_l) \right],

where, l = 1, \dots, L: The number of partitions. c_l: The threshold for the l-th variable. x_{pl} \leq c_l and x_{pl} > c_l: The subgroups defined by tree partitions. I(\cdot): The indicator function (1 if true, 0 otherwise). \gamma_{ik} and \gamma_{ir}: Subgroup-specific intercepts for logistic regression models in partitioned regions. The terminal or leaf nodes of the tree represent the final groups of patients with similar response patterns. The IFT model assumes unidimensionality, and the covariates x_{pl} can be either continuous or categorical.

If an item is never chosen for splitting, it is assumed to be free of DIF. The equation for an item free of DIF can be defined as:

\eta_{pi} = \beta_i S_p + \beta_0i,

Value

A list containing:

Author(s)

Muditha L. Bodawatte Gedara (muditha.lakmali.1993@gmail.com), Barret A. Monchka, Lisa M. Lix

References

Berger, Moritz and Tutz, Gerhard (2016): Detection of Uniform and Non-Uniform Differential Item Functioning by Item Focused Trees, Journal of Educational and Behavioral Statistics 41(6), 559-592.

See Also

DIFtree for training the DIFtree model.

Examples

if (requireNamespace("DIFtree", quietly = TRUE)) {
  # Load DIFtree
  library(DIFtree)

# Load the dataset
data("mydata", package = "IFTPredictor")

# Observe the data
head(mydata)

# Extract response and covariate data
mydata<-mydata[,c(4:6,21:23)] # Items 4 to 6 will be tested for DIF across covariates 21 to 23
Y <- mydata[, 1:3]  # Specify items you want to test for DIF (i.e.,items 1 to 3)
X <- mydata[, 4:6]  # Covariates

# Create total score column calculating total item score for each patient
mydata$total_score <- rowSums(mydata[, 1:3])

# Fit the DIFtree model (Y = response data, X = covariate data)
mod <- DIFtree(Y, X, model = "Logistic", type = "udif", alpha = 0.05, nperm = 5, trace = TRUE)

# Predict item responses using the model and the total score
result <- predict_item_responses(mod, dataset = mydata, total_score = "total_score")

} else {
  message("The 'DIFtree' package is not installed. Please install it to run this example.")
}