Insights from Reparameterized DINA and Beyond

Abstract

The purpose of cognitive diagnosis is to obtain information about the set of skills or attributes that examinees have or do not have. A cognitive diagnostic model (CDM) attempts to extract this information from the pattern of responses of examinees to test items. A number of general CDMs have been proposed, such as the general diagnostic model (GDM; von Davier M, Brit J Math Stat Psychol 61:287–307, 2008), the generalized DINA model (GDINA; de la Torre J, Psychometrika 76:179–199, 2011), and the log-linear cognitive diagnostic model (LCDM; Henson RA, Templin JL, Willse JT, Psychometrika 74:191–210, 2009). These general models can be shown to include well-known models that are often used in cognitive diagnosis, such as the deterministic inputs noisy and gate model (DINA; Junker BW, Sijtsma K, Appl Psychol Meas 25:258–272, 2001), the deterministic inputs noise or gate model (DINO; Templin JL, Henson RA, Psychol Methods 11:287–305, 2006), the additive cognitive diagnosis model (ACDM; de la Torre J, Psychometrika 76:179–199, 2011), the linear logistic model (LLM; Maris E, Psychometrika 64:187–212, 1999), and the reduced reparameterized unified model (rRUM; Hartz SM, A Bayesian framework for the unified model for assessing cognitive abilities. Unpublished doctoral dissertation, 2002). This chapter starts with a simple reparameterized version of the DINA model and builds up to other models; all of the models are shown to be extensions or variations of the basic model. Working up to more general models from a simple form helps to illustrate basic aspects of the models and associated concepts, such as the meaning of model parameters, issues of estimation, monotonicity, duality, and the relation of the models to each other and more general forms. In addition, reparameterizing CDMs as latent class models allows one to use standard software for latent class analysis (LCA), which offers a connection to latent class analysis and also allows one to take advantage of recent advances in LCA.