GDINA-package: The Generalized DINA Model Framework

Description Details Author(s) References See Also


For conducting CDM analysis within the G-DINA model framework


This package provides a framework for a series of cognitive diagnostic analyses for dichotomous and polytomous responses.

Various cognitive diagnosis models (CDMs) can be calibrated using the GDINA function, including the G-DINA model, the deterministic inputs, noisy and gate (DINA; de la Torre, 2009; Junker & Sijtsma, 2001) model, the deterministic inputs, noisy or gate (DINO; Templin & Henson, 2006) model, the reduced reparametrized unified model (R-RUM; Hartz, 2002), the additive CDM (A-CDM; de la Torre, 2011), and the linear logistic model (LLM; Maris, 1999;).Note that the LLM is also called compensatory RUM and the RRUM is equivalent to the generalized NIDA model.

For ordinal and nominal responses, the sequential G-DINA model (Ma, & de la Torre, 2016) is fitted and all aforementioned CDMs can be used as the processing function at the category level. Different CDMs can be assigned to different items within a single assessment. Item parameters are estimated using the MMLE/EM algorithm. Details about the estimation algorithm can be found in de la Torre (2009), de la Torre (2011), Ma, Iaconangelo, & de la Torre (2016) and Ma, & de la Torre (2016). The higher-order attribute structure (de la Torre, & Douglas, 2004), polytomous attributes (Chen, & de la Torre, 2013) and attribute structures (e.g., linear, divergent) can also be accommodated. Monotonicity constraints for item/category success probabilities can also be specified.

Q-matrix validation (de la Torre, & Chiu, 2016; see Qval), item and model fit statistics (Chen, de la Torre, & Zhang, 2013; see itemfit), model comparison at test and item level (de la Torre, & Lee, 2013; Ma, Iaconangelo, & de la Torre, 2016; see modelcomp), and differential item functioning (Hou, de la Torre, & Nandakumar, 2014; see dif) can also be conducted.


Wenchao Ma, Rutgers University, [email protected]
Jimmy de la Torre, The University of Hong Kong


Chen, J., & de la Torre, J. (2013). A General Cognitive Diagnosis Model for Expert-Defined Polytomous Attributes. Applied Psychological Measurement, 37, 419-437.

Chen, J., de la Torre, J., & Zhang, Z. (2013). Relative and Absolute Fit Evaluation in Cognitive Diagnosis Modeling. Journal of Educational Measurement, 50, 123-140.

de la Torre, J. (2009). DINA Model and Parameter Estimation: A Didactic. Journal of Educational and Behavioral Statistics, 34, 115-130.

de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76, 179-199.

de la Torre & Chiu. (2016). A General Method of Empirical Q-matrix Validation. Psychometrika, 81, 253-273.

de la Torre, J., & Douglas, J. A. (2004). Higher-order latent trait models for cognitive diagnosis. Psychometrika, 69, 333-353.

de la Torre, J., & Lee, Y. S. (2013). Evaluating the wald test for item-level comparison of saturated and reduced models in cognitive diagnosis. Journal of Educational Measurement, 50, 355-373.

Haertel, E. H. (1989). Using restricted latent class models to map the skill structure of achievement items. Journal of Educational Measurement, 26, 301-321.

Hartz, S. M. (2002). A bayesian framework for the unified model for assessing cognitive abilities: Blending theory with practicality (Unpublished doctoral dissertation). University of Illinois at Urbana-Champaign.

Hou, L., de la Torre, J., & Nandakumar, R. (2014). Differential item functioning assessment in cognitive diagnostic modeling: Application of the Wald test to investigate DIF in the DINA model. Journal of Educational Measurement, 51, 98-125.

Junker, B. W., & Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25, 258-272.

Ma, W., & de la Torre, J. (2016). A sequential cognitive diagnosis model for polytomous responses. British Journal of Mathematical and Statistical Psychology. 69, 253-275.

Ma, W., Iaconangelo, C., & de la Torre, J. (2016). Model similarity, model selection and attribute classification. Applied Psychological Measurement, 40, 200-217.

Maris, E. (1999). Estimating multiple classification latent class models. Psychometrika, 64, 187-212.

See Also

CDM for estimating G-DINA model and a set of other CDMs; ACTCD and NPCD for nonparametric CDMs; dina for DINA model in Bayesian framework

Wenchao-Ma/GDINA documentation built on June 24, 2017, 11:57 a.m.