It is common to find mixed-format data results from the use of both multiple-choice (MC) and constructed-response (CR) questions on assessments. Dealing with these mixed response types involves understanding what the assessment is measuring, and the use of suitable measurement models to estimate latent abilities. Past research in educational…

This software review discusses the capabilities of Stata to conduct item response theory modeling. The commands needed for fitting the popular one-, two-, and three-parameter logistic models are initially discussed. The procedure for testing the discrimination parameter equality in the one-parameter model is then outlined. The commands for fitting…

The property of item parameter invariance in item response theory (IRT) plays a pivotal role in the applications of IRT such as test equating. The scope of parameter invariance when using estimates from finite biased samples in the applications of IRT does not appear to be clearly documented in the IRT literature. This article provides information…

Current methods that simultaneously model differential testlet functioning (DTLF) and differential item functioning (DIF) constrain the variances of latent ability and testlet effects to be equal between the focal and the reference groups. Such a constraint can be stringent and unrealistic with real data. In this study, we propose a multigroup…

Diagnostic classification models (DCMs, also known as cognitive diagnosis models) hold the promise of providing detailed classroom information about the skills a student has or has not mastered. Specifically, DCMs are special cases of constrained latent class models where classes are defined based on mastery/nonmastery of a set of attributes (or…

Analyzing students' growth remains an important topic in educational research. Most recently, Diagnostic Classification Models (DCMs) have been used to track skill acquisition in a longitudinal fashion, with the purpose to provide an estimate of students' learning trajectories in terms of the change of fine-grained skills overtime. Response time…

Goldhammer (this issue) proposes an interesting approach to dealing with the speededness of item responses. Rather than modeling speed as a latent variable that varies from person to person, he proposes to use experimental conditions that are expected to fix the speed, thereby eliminating individual differences on this dimension in order to make…

The main challenge of ability tests relates to the difficulty of items, whereas speed tests demand that test takers complete very easy items quickly. This article proposes a conceptual framework to represent how performance depends on both between-person differences in speed and ability and the speed-ability compromise within persons. Related…

In this rejoinder, Maydeu-Olivares states that, in item response theory (IRT) measurement applications, the application of goodness-of-fit (GOF) methods informs researchers of the discrepancy between the model and the data being fitted (the room for improvement). By routinely reporting the GOF of IRT models, together with the substantive results…

Mroch, Suh, Kane, & Ripkey (2009); Suh, Mroch, Kane, & Ripkey (2009); and Kane, Mroch, Suh, & Ripkey (2009) provided elucidating discussions on critical properties of linear equating methods under the nonequivalent groups with anchor test (NEAT) design. In this popular equating design, two test forms are administered to different…

This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…

This paper addresses two problems relating to the interpretability of the model parameters in the three parameter logistic model. First, it is shown that if the values of the discrimination parameters are all the same, the remaining parameters are nonidentifiable in a nontrivial way that involves not only ability and item difficulty, but also the…

In the following, I confine my comments mainly to the issue of invariance in relation to Rasch's model for dichotomous, ability test items. "It is senseless to seek in the logical process of mathematical elaboration a psychologically significant precision that was not present in the psychological setting of the problem." (Boring, 1920)

In this commentary, the author points out few issues, one being that there are models mislabeled as diagnostic, which deal with linear decompositions of item difficulties rather than estimating multidimensional skill variables. The author discusses the issue that there are many new names for essentially well-known models for multiple simultaneous…

As Rupp and Templin (2008) stated directly, diagnostic classification methods "are confirmatory in nature." Methods, though, are neither inherently confirmatory nor exploratory. Diagnostic classification modeling, with its analytical and computational obstacles eventually yielding as a comprehensive and potent discipline emerges, will…