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 Unpublished doctoral dissertation, 2002).