Date of Award


Document Type

Open Access Thesis



First Advisor

Brian T Habing


Diagnostic classification models (DCMs) are structured latent class models widely discussed in the field of psychometrics. They model subjects' underlying attribute patterns and classify subjects into unobservable groups based on their mastery of attributes required to answer the items correctly. The effective implementation of DCMs depends on correct specification of a Q-matrix which is a binary matrix linking attribute patterns to items. Current literature on assessing the appropriateness of Q-matrix specifications has focused on validation methods for the deterministic-input, noisy-and-gate (DINA) model. The goal of the study is to develop general Q-matrix validation methods that can be applied to a wider class of DCMs. The study proposes a two-stage validation method which incorporates the idea of sequential searching based on the posterior distribution of attribute patterns and Bayesian model selection techniques. Simulation studies show that the proposed methods successfully detect and correct misspecifications in a Q-matrix for a complicated non-compensatory DCM, the reduced reparameterized unified model (RUM), and a compensatory DCM, the deterministic input, noisy-or-gate (DINO) model.

Model estimation is the first step in validating a Q-matrix. The EM algorithm is shown to provide accurate estimates for the reduced RUM, with the advantage of significant computational time savings compared to estimation by Markov chain Monte Carlo (MCMC). In addition, factors affecting the performance of the validation methods are discussed. Suggestions on implementation of the methods under the case when items are from a combination of DCMs are given.