In this article, we extend Liao's test for across-group comparisons of the fixed effects from the generalized linear model to the fixed and random effects of the generalized linear mixed model (GLMM). Using as our basis the Wald statistic, we developed an asymptotic test statistic for across-group comparisons of these effects. The test can be…

Understanding whether or not different types of students master various attributes can aid future learning remediation. In this study, two-level diagnostic classification models (DCMs) were developed to represent the probabilistic relationship between external latent classes and attribute mastery patterns. Furthermore, variational Bayesian (VB)…

As with any psychometric models, the validity of inferences from cognitive diagnosis models (CDMs) determines the extent to which these models can be useful. For inferences from CDMs to be valid, it is crucial that the fit of the model to the data is ascertained. Based on a simulation study, this study investigated the sensitivity of various fit…

The article considers a test of specification for quantile regressions. The test relies on the increase of the objective function and the worsening of the fit when unnecessary constraints are imposed. It compares the objective functions of restricted and unrestricted models and, in its different formulations, it verifies (a) forecast ability, (b)…

Diagnostic score reports linking assessment outcomes to instructional interventions are one of the most requested features of assessment products. There is a body of interesting work done in the last 20 years including Tatsuoka's rule space method (Tatsuoka, 1983), Haertal and Wiley's binary skills model (Haertal, 1984; Haertal & Wiley, 1993),…

Assessing fit of psychometric models has always been an issue of enormous interest, but there exists no unanimously agreed upon item fit diagnostic for the models. Bayesian networks, frequently used in educational assessments (see, for example, Mislevy, Almond, Yan, & Steinberg, 2001) primarily for learning about students' knowledge and…