%0 Journal Article
%T Diagnostic Classification Models for Testlets: Methods and Theory.
%A Xu X
%A Fang G
%A Guo J
%A Ying Z
%A Zhang S
%J Psychometrika
%V 0
%N 0
%D 2024 Mar 26
%M 38528268
%F 2.29
%R 10.1007/s11336-024-09962-9
%X Diagnostic classification models (DCMs) have seen wide applications in educational and psychological measurement, especially in formative assessment. DCMs in the presence of testlets have been studied in recent literature. A key ingredient in the statistical modeling and analysis of testlet-based DCMs is the superposition of two latent structures, the attribute profile and the testlet effect. This paper extends the standard testlet DINA (T-DINA) model to accommodate the potential correlation between the two latent structures. Model identifiability is studied and a set of sufficient conditions are proposed. As a byproduct, the identifiability of the standard T-DINA is also established. The proposed model is applied to a dataset from the 2015 Programme for International Student Assessment. Comparisons are made with DINA and T-DINA, showing that there is substantial improvement in terms of the goodness of fit. Simulations are conducted to assess the performance of the new method under various settings.