Recent developments have enabled the modeling of longitudinal assessment data in a diagnostic classification model (DCM) framework. These longitudinal DCMs were developed to provide measures of student growth on a discrete scale in the form of attribute mastery transitions, thereby supporting categorical and criterion-referenced interpretations of…

Growth mixture models (GMMs) are prevalent for modeling unknown population heterogeneity via distinct latent classes. However, GMMs are riddled with convergence issues, often requiring researchers to atheoretically alter the model with cross-class constraints to obtain convergence. We discuss how within-class random effects in GMMs exacerbate…

Misclassification means the observed category is different from the underlying one and it is a form of measurement error in categorical data. The measurement error in continuous, especially normally distributed, data is well known and studied in the literature. But the misclassification in a binary outcome variable has not yet drawn much attention…

Test scores are commonly reported in a small number of ordered categories. Examples of such reporting include state accountability testing, Advanced Placement tests, and English proficiency tests. This paper introduces and evaluates methods for estimating achievement gaps on a familiar standard-deviation-unit metric using data from these ordered…