Hierarchical mixtures of diagnostic models

Psychological testing aims at making inferences about individual differences or the estimation of distributions of psychological constructs in groups of interest. However, a test instrument’s relationship to the construct, the actual variable of interest, may change across subpopulations, or the instrument’s measurement accuracy is not the same across subpopulations. This paper introduces an extension of the mixture distribution general diagnostic model (GDM) that allows studying the population dependency of multidimensional latent trait models across observed and latent populations. Note that so-called diagnostic models do not aim at diagnosing individual test takers in the sense of a clinical diagnosis, or an extended case-based examination using multiple test instruments. The term cognitive diagnosis was coined following the development of models that attempt to identify (diagnose?) more than a single skill dimension. The GDM is a general modeling framework for confirmatory multidimensional item response models and includes well-known models such as item response theory (IRT), latent class analysis (LCA), and located latent class models as special cases. The hierarchical extensions of the GDM presented in this paper enable one to check the impact of clustered data, such as data from students with different native language background taking an English language test, on the structural parameter estimates of the GDM. Moreover, the hierarchical version of the GDM allows the examination of differences in skill distributions across these clusters.