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PSYCHOMETRIKAVOL. 76, NO. 2, 179199
APRIL 2011
DOI: 10.1007/S11336-011-9207-7
THE GENERALIZED DINA MODEL FRAMEWORK
JIMMY DE LA TORRE
RUTGERS, THE STATE UNIVERSITY OF NEW JERSEY
The G-DINA (generalized deterministic inputs, noisy and gate) model is a generalization of the DINA model with more relaxed assumptions. In its saturated form, the G-DINA model is equivalent to other general models for cognitive diagnosis based on alternative link functions. When appropriate constraints are applied, several commonly used cognitive diagnosis models (CDMs) can be shown to be special cases of the general models. In addition to model formulation, the G-DINA model as a general CDM framework includes a component for item-by-item model estimation based on design and weight matrices, and a component for item-by-item model comparison based on the Wald test. The paper illustrates the estimation and application of the G-DINA model as a framework using real and simulated data. It concludes by discussing several potential implications of and relevant issues concerning the proposed framework.
Key words: cognitive diagnosis, DINA, MMLE, parameter estimation, Wald test, model comparison.
1. Overview and Background
Cognitive diagnosis models (CDMs) are latent variable models developed primarily for assessing student mastery and non-mastery on a set of ner-grained skills. In the CDM literature, skills have been generically referred to as attributes, and are represented by the binary vector . Several specic and general CDMs of various formulations have been proposed in the psycho-metric literature. Examples of specic CDMs include the deterministic inputs, noisy and gate (DINA; de la Torre, 2009b; Junker & Sijtsma, 2001), and the reduced reparametrized unied model (R-RUM; Hartz, 2002; Roussos, DiBello, Stout, Hartz, Henson, & Templin, 2007); examples of general CDMs include the log-linear CDM (Henson, Templin, & Willse, 2009), and the general diagnostic model (GDM; von Davier, 2005). However, it is not entirely clear whether the different CDM formulations represent different classes of models, or to what extent these models are related to one another. In addition, simultaneously estimating the parameters of the models with disparate formulations and comparing their relative t at the item level have remained challenging tasks. To address these issues, this paper proposes a framework for (1) relating several CDMs with different formulations, (2) estimating the parameters of multiple CDMs specied within a single test, and...