Joint modeling of response accuracy and time in process data: A multilevel latent class IRT model

Luca Brusa · Francesco Bartolucci · Fulvia Pennoni · Giorgio Vittadini

The RTMLC package contains functions to specify and estimate Response Time Multilevel Latent Class (RTMLC) model for the joint analysis of response accuracy and response time in item-response data. The model is designed for dichotomously scored items administered to individuals nested within higher-level units, such as students within school classes.

The proposed framework relies on discrete latent variables at both the individual and cluster levels, allowing unobserved heterogeneity to be represented through latent classes. Response accuracy is modeled through a normal-ogive IRT sub-model, whereas response times are modeled by a log-normal sub-model. Individual- and cluster-level covariates can be included in both sub-models.

The code implements maximum likelihood estimation through the Expectation-Maximization algorithm. It also allows for structurally missing item responses arising from the random assignment of item subsets from a larger item pool.

To install the RTMLC package directly from GitHub:

if (!requireNamespace("pak", quietly = TRUE))
  install.packages("pak")
pak::pkg_install("LB1304/RTMLC")
library(RTMLC)

To download the .tar.gz file (for manual installation), use this link.

The package includes three main user-level functions:

• Draw.RTMLC, which generates simulated multilevel item-response data with response accuracy and response times under the RTMLC model;
• Est.RTM, which estimates the baseline response accuracy and response time model without latent classes and can be used to obtain initial values for the full model;
• Est.RTMLC, which estimates the full Response Time Multilevel Latent Class IRT model for a specified number of cluster- and individual-level latent classes.

More details on the available options are accessible with the commands:

help("Draw.RTMLC")
help("Est.RTM")
help("Est.RTMLC")

A small reproducible example based on simulated data is available in examples/example.R. The example illustrates how to generate data, estimate the baseline RTM model, estimate the full RTMLC model, and inspect the main estimated parameters.