This article critically reviews how diagnostic models have been conceptualized and how they compare to other approaches used in educational measurement. In particular, certain assumptions that have been taken for granted and used as defining characteristics of diagnostic models are reviewed and it is questioned whether these assumptions are the…

In their 2016 work, Aguirre-Urreta et al. provided a contribution to the literature on causal measurement models that enhances clarity and stimulates further thinking. Aguirre-Urreta et al. presented a form of statistical identity involving mapping onto the portion of the parameter space involving the nomological net, relationships between the…

We review the GIDNA and CDM packages in R for fitting cognitive diagnosis/diagnostic classification models. We first provide a summary of their core capabilities and then use both simulated and real data to compare their functionalities in practice. We found that the most relevant routines in the two packages appear to be more similar than…

We describe an application of the assessment triangle, using a learning progression as the "cognition" vertex. We summarize two studies to evaluate whether evidence of student performance is consistent with our progression. In Study 1, we conducted think alouds using draft assessment activities and evaluated responses in relation to the…

Von Davier, Naemi, and Roberts (this issue) present a nice summary of the statistical ambiguity often encountered in making distinctions between qualitative and quantitative constructs. In this commentary, the author begins with two broad points. The first is that the mixture/factor arguments are most intriguing when firmly embedded in a…

The notion that there is often no clear distinction between factorial and typological models (von Davier, Naemi, & Roberts, this issue) is sound. As von Davier et al. state, theory often indicates a preference between these models; however the statistical criteria by which these are delineated offer much less clarity. In many ways the procedure…

In the focus article of this issue, von Davier, Naemi, and Roberts essentially coupled: (1) a short methodological review of structural similarities of latent variable models with discrete and continuous latent variables; and (2) 2 short empirical case studies that show how these models can be applied to real, rather than simulated, large-scale…

Von Davier et al. (this issue) describe two analyses that aim at determining whether the constructs measured with a number of observed items are categorical or continuous in nature. The issue of types versus traits has a long history and is relevant in many areas of behavioral research, including personality research, as emphasized by von Davier…

"Diagnostic classification models" (DCM) are frequently promoted by psychometricians as important modelling alternatives for analyzing response data in situations where multivariate classifications of respondents are made on the basis of multiple postulated latent skills. In this review paper, a definitional boundary of the space of DCM…