IRTrees: Tree-Based Item Response Models of the GLMM Family

Abstract

A category of item response models is presented with two defining features: they all (i) have a tree representation, and (ii) are members of the family of generalized linear mixed models (GLMM). Because the models are based on trees, they are denoted as IRTree models. The GLMM nature of the models implies that they can all be estimated with the glmer function of the lme4 package in R. The aim of the article is to present four subcategories of models, the first two of which are based on a tree representation for response categories: 1. linear response tree models (e.g., missing response models), 2. nested response tree models (e.g., models for parallel observations regarding item responses such as agreement and certainty), while the last two are based on a tree representation for latent variables: 3. linear latent-variable tree models (e.g., models for change processes), and 4. nested latent-variable tree models (e.g., bi-factor models). The use of the glmer function is illustrated for all four subcategories. Simulated example data sets and two service functions useful in preparing the data for IRTree modeling with glmer are provided in the form of an R package, irtrees. For all four subcategories also a real data application is discussed.

Use of Response Time for Measuring Cognitive Ability

“…They dichotomized each individual's response times (from a verbal analogies and a progressive matrices test) into a fast vs. slow category, based either on the person's median or on the median response time to each item, yielding fast-correct, fast-incorrect, slow-correct, and slow-incorrect response categories. They then fit a 1PL IRTree model [129], and found that three different latent traits were required to fit the data: speed, slow intelligence, and fast intelligence. They also found that although fast and slow intelligence were highly correlated, they were distinguishable.…”

Predator mimicry, not conspicuousness, explains the efficacy of butterfly eyespots

“…In order to allow quantitative analysis of the categorical responses to the treatments, we analysed them using item response tree GLMMs [29]. This technique, borrowed from sociometrics, can be adapted and used as a way to handle categorical data of behaviour [30].…”

A generalized item response tree model for psychological assessments

“…These prior approaches, however, have some limitations. For instance, the models proposed by De Boeck and Partchev (2012) do not allow for trees with more than two branches and rely on one-parameter logistic models, while Bockenholt (2012) is based on one-parameter probit models.…”