Fitting Diffusion Item Response Theory Models for Responses and Response Times Using theRPackagediffIRT

Abstract

In the psychometric literature, item response theory models have been proposed that explicitly take the decision process underlying the responses of subjects to psychometric test items into account. Application of these models is however hampered by the absence of general and flexible software to fit these models. In this paper, we present diffIRT, an R package that can be used to fit item response theory models that are based on a diffusion process. We discuss parameter estimation and model fit assessment, show the viability of the package in a simulation study, and illustrate the use of the package with two datasets pertaining to extraversion and mental rotation. In addition, we illustrate how the package can be used to fit the traditional diffusion model (as it has been originally developed in experimental psychology) to data.

Trait Characteristics of Diffusion Model Parameters

“…Several authors have previously suggested an integration of item response theory (IRT) and the diffusion model into a latent variable model, which takes into account that the mean drift rate consists of a person part and an item part [32][33][34]. It has been shown that diffusion IRT models can account for psychometric responses on tests of bipolar traits [33] as well as for ability tests under the assumption that abilities have a natural zero point [34].…”

Use of Response Time for Measuring Cognitive Ability

“…Decision making is fastest for those high or low on the trait (a "distance-difficulty" hypothesis [31,117]), and increasing the time limit will make low (high) trait respondents less (more) likely to say yes. A marginal maximum likelihood estimation approach for the D-and Q-diffusion models has been implemented in an R package, diffIRT [118].…”

“…", or "are you outgoing or reserved? "), can be modeled with approaches used in cognitive tasks, such as a diffusion model [70,71,118], or a simpler 1PL model [6], in which the item difficulty pertains to the difficulty of the choice one makes in deciding whether a word or statement describes oneself appropriately or not.…”

Analysing model fit of psychometric process models: An overview, a new test and an application to the diffusion model

“…Several tests for the fit of psychometric process models – among them those of Molenaar et al . (), Ranger and Kuhn () and Ranger et al . () – can be shown to be variants of the generalized moment test.…”

“…Similar to the M 2 test of Molenaar et al . (), the M ULS test is a test of global fit. It improves upon the former test by considering response times in addition to the responses.…”