This paper presents a mixture item response tree (IRTree) model for extreme response style. Unlike traditional applications of single IRTree models, a mixture approach provides a way of representing the mixture of respondents following different underlying response processes (between individuals), as well as the uncertainty present at the individual level (within an individual). Simulation analyses reveal the potential of the mixture approach in identifying subgroups of respondents exhibiting response behavior reflective of different underlying response processes. Application to real data from the Students Like Learning Mathematics (SLM) scale of Trends in International Mathematics and Science Study (TIMSS) 2015 demonstrates the superior comparative fit of the mixture representation, as well as the consequences of applying the mixture on the estimation of content and response style traits. We argue that methodology applied to investigate response styles should attend to the inherent uncertainty of response style influence due to the likely influence of both response styles and the content trait on the selection of extreme response categories.

We consider a multidimensional noncompensatory approach for binary items in passage-based tests. The passage-based noncompensatory model (PB-NM) emphasizes two underlying components in solving passage-based test items: a passage-related component and a passage-independent component. An advantage of the PB-NM model over commonly applied compensatory models (e.g., bifactor model) is that the two components are parameterized in relation to difficulty as opposed to discrimination parameters. As a result, while simultaneously accounting for passage-related local item dependence, the model permits the assessment of how items based on the same passage may require varying levels of passage comprehension (as well as varying levels of passage-independent proficiency) to obtain a correct response. Through a simulation study, we evaluate the comparative fit of the PB-NM against the bifactor model and also illustrate the relationship between the difficulty parameters of the PB-NM and the discrimination parameters of the bifactor model. We further apply the PB-NM to an actual reading comprehension test to demonstrate the relevance of the model in understanding variation in the relative difficulty of the two components across different item types.

There recently have been many studies examining conditional dependence between response accuracy and response times in cognitive tests. While most previous research has focused on revealing a general pattern of conditional dependence for all respondents and items, it is plausible that the pattern may vary across respondents and items. In this paper, we attend to its potential heterogeneity and examine the item and person specificities involved in the conditional dependence between item responses and response times. To this end, we use a latent space item response theory (LSIRT) approach with an interaction map that visualizes conditional dependence in response data in the form of item–respondent interactions. We incorporate response time information into the interaction map by applying LSIRT models to slow and fast item responses. Through empirical illustrations with three cognitive test datasets, we confirm the presence and patterns of conditional dependence between item responses and response times, a result consistent with previous studies. Our results further illustrate the heterogeneity in the conditional dependence across respondents, which provides insights into understanding individuals’ underlying item-solving processes in cognitive tests. Some practical implications of the results and the use of interaction maps in cognitive tests are discussed.

Item response theory (IRT) models usually assume that latent traits follow normal distributions. Nonetheless, violations of the normality assumption are not uncommon in psychology and psychiatry. While several studies have investigated the impact of non-normality on parameter estimation for some IRT models, bifactor models for polytomous data have been largely excluded despite their increasing popularity in psychology and education. Existing findings on other IRT models may not apply to bifactor models because of their unique characteristics. In this study, we examined the impact of latent trait non-normality on parameter estimation in the bifactor graded response model using a simulation study. The results indicate that (1) general-factor non-normality primarily affected item parameter estimates associated with the general factor but not specific factors, (2) specific-factor non-normality showed smaller and more localized effects, primarily on bias in specific-factor discrimination and intercept estimates; and (3) despite the misspecification of latent trait priors, maximum a posteriori estimates of latent traits tend to be more stable than the maximum likelihood estimates. Implications of the findings are discussed.