A Monte Carlo simulation study was conducted to examine the performance of [alpha], [lambda]2, [lambda][subscript 4], [lambda][subscript 2], [omega][subscript T], GLB[subscript MRFA], and GLB[subscript Algebraic] coefficients. Population reliability, distribution shape, sample size, test length, and number of response categories were varied…

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…

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…

The paper by Rupp and Templin (2008) is an excellent work on the characteristics and features of cognitive diagnostic models (CDM). In this article, the authors comment on some substantial and methodological aspects of this focus paper. They organize their comments by going through issues associated with the terms "cognitive,"…

Diagnostic assessment is currently an active research area in educational measurement. Literature related to diagnostic modeling has been in existence for several decades, but a great deal of research has been conducted within the last decade or so, especially within the last five years. The author summarizes the key components in the application…

In this commentary, the author addresses what is referred to as the deterministic input, noisy "and" gate (DINA) model. The author mentions concerns with how this model has been formulated and presented. In particular, the author points out that there is a lack of recognition of the confounding of profiles that generally arises and then discusses…

On a general level, the objective of diagnostic classifications models (DCMs) lies in a classification of individuals regarding multiple latent skills. In this article, the authors show that this objective can be achieved by multidimensional adaptive testing (MAT) as well. The authors discuss whether or not the restricted applicability of DCMs can…

In this paper, the authors complete the summative stage of the validity argument approach, then use their experiences to reflect on the validity argument as a method. They begin by evaluating the inferences and assumptions of the interpretive argument for the MKT measures. Then they examine both the form and the structure of the interpretive…

Validation efforts typically focus around what, exactly, is measured by an instrument(s), and whether what is measured corresponds to the theoretical domain(s) originally specified. The authors' goal for this article is to build instruments focused around measuring the mathematical knowledge used in teaching: not only the content that teachers…

This paper provides a summary of the authors' attempts to uncover links between their measures, classroom mathematics instruction, and student learning. This paper also provides evidence regarding one central critique of their measures: that multiple-choice assessments cannot validly represent the knowledge, skills, and judgment involved in actual…