The purpose of this ITEMS module is to provide an introduction to differential item functioning (DIF) analysis using mixture item response models. The mixture item response models for DIF analysis involve comparing item profiles across latent groups, instead of manifest groups. First, an overview of DIF analysis based on latent groups, called…

Multilevel modeling (MLM) is frequently used to detect group differences, such as an intervention effect in a pre-test--post-test cluster-randomized design. Group differences on the post-test scores are detected by controlling for pre-test scores as a proxy variable for unobserved factors that predict future attributes. The pre-test and post-test…

In the presence of test speededness, the parameter estimates of item response theory models can be poorly estimated due to conditional dependencies among items, particularly for end-of-test items (i.e., speeded items). This article conducted a systematic comparison of five-item calibration procedures--a two-parameter logistic (2PL) model, a…

Current methods for detecting growth of students' problem-solving skills in math focus mainly on analyzing changes in test scores. Score-level analysis, however, may fail to reflect subtle changes that might be evident at the item level. This article demonstrates a method for studying item-level changes using data from a multiwave experiment with…

Mixture item response theory models have been suggested as a potentially useful methodology for identifying latent groups formed along secondary, possibly nuisance dimensions. In this article, we describe a multilevel mixture item response theory (IRT) model (MMixIRTM) that allows for the possibility that this nuisance dimensionality may function…

A multilevel latent transition analysis (LTA) with a mixture IRT measurement model (MixIRTM) is described for investigating the effectiveness of an intervention. The addition of a MixIRTM to the multilevel LTA permits consideration of both potential heterogeneity in students' response to instructional intervention as well as a methodology for…