For conducting CDM analysis within the G-DINA model framework


This package (Ma & de la Torre, 2020a) provides a framework for a series of cognitively diagnostic analyses for dichotomous and polytomous responses.

Various cognitive diagnosis models (CDMs) can be calibrated using the GDINA function, including the G-DINA model (de la Torre, 2011), 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), the multiple-strategy DINA model (de la Torre, & Douglas, 2008) and models defined by users under the G-DINA framework using different link functions and design matrices (de la Torre, 2011). 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) can be fitted and most of the aforementioned CDMs can be used as the processing functions (Ma, & de la Torre, 2016) 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 Ma and de la Torre (2020). The joint attribute distribution can be modeled using an independent model, a higher-order IRT model (de la Torre, & Douglas, 2004), a loglinear model (Xu & von Davier, 2008), a saturated model or a hierarchical structures (e.g., linear, divergent). Monotonicity constraints for item/category success probabilities can also be specified.

In addition, to handle multiple strategies, generalized multiple-strategy CDMs for dichotomous response (Ma & Guo, 2019) can be fitted using GMSCDM function and diagnostic tree model (Ma, 2019) can also be estimated using DTM function for polytomous responses. Note that these functions are experimental, and are expected to be further extended in the future. Other diagnostic approaches include the multiple-choice model (de la Torre, 2009) and an iterative latent class analysis (ILCA; Jiang, 2019).

Various Q-matrix validation methods (de la Torre, & Chiu, 2016; de la Torre & Ma, 2016; Ma & de la Torre, 2020b; Najera, Sorrel, & Abad, 2019; see Qval), model-data fit statistics (Chen, de la Torre, & Zhang, 2013; Hansen, Cai, Monroe, & Li, 2016; Liu, Tian, & Xin, 2016; Ma, 2020; see modelfit and itemfit), model comparison at test and item level (de la Torre, 2011; de la Torre, & Lee, 2013; Ma, Iaconangelo, & de la Torre, 2016; Ma & de la Torre, 2019; Sorrel, Abad, Olea, de la Torre, & Barrada, 2017; Sorrel, de la Torre, Abad, & Olea, 2017; see modelcomp), and differential item functioning (Hou, de la Torre, & Nandakumar, 2014; Ma, Terzi, Lee, & de la Torre, 2017; see dif) can also be conducted.

To use the graphical user interface, check startGDINA.


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, J. & Chiu, C-Y. (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., & Douglas, J. A. (2008). Model evaluation and multiple strategies in cognitive diagnosis: An analysis of fraction subtraction data. Psychometrika, 73, 595.

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.

de la Torre, J., & Ma, W. (2016, August). Cognitive diagnosis modeling: A general framework approach and its implementation in R. A Short Course at the Fourth Conference on Statistical Methods in Psychometrics, Columbia University, New York.

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. (2019). A diagnostic tree model for polytomous responses with multiple strategies. British Journal of Mathematical and Statistical Psychology, 72, 61-82.

Ma, W. (2020). Evaluating the fit of sequential G-DINA model using limited-information measures. Applied Psychological Measurement, 44, 167-181.

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., & de la Torre, J. (2019). Category-Level Model Selection for the Sequential G-DINA Model. Journal of Educational and Behavioral Statistics. 44, 61-82.

Ma, W., & de la Torre, J. (2019). Digital Module 05: Diagnostic measurement-The G-DINA framework. Educational Measurement: Issues and Practice, 39, 114-115.

Ma, W., & de la Torre, J. (2020a). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.

Ma, W., & de la Torre, J. (2020b). An empirical Q-matrix validation method for the sequential G-DINA model. British Journal of Mathematical and Statistical Psychology, 73, 142-163.

Ma, W., & Guo, W. (2019). Cognitive diagnosis models for multiple strategies. British Journal of Mathematical and Statistical Psychology, 72, 370-392.

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

Ma, W., Terzi, R., Lee, S., & de la Torre, J. (2017, April). Multiple group cognitive diagnosis models and their applications in detecting differential item functioning. Paper presented at the Annual Meeting ofthe American Educational Research Association, San Antonio, TX.

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

Najera, P., Sorrel, M., & Abad, P. (2019). Reconsidering Cutoff Points in the General Method of Empirical Q-Matrix Validation. Educational and Psychological Measurement.

Sorrel, M. A., Abad, F. J., Olea, J., de la Torre, J., & Barrada, J. R. (2017). Inferential Item-Fit Evaluation in Cognitive Diagnosis Modeling. Applied Psychological Measurement, 41, 614-631.

Sorrel, M. A., de la Torre, J., Abad, F. J., & Olea, J. (2017). Two-Step Likelihood Ratio Test for Item-Level Model Comparison in Cognitive Diagnosis Models. Methodology, 13, 39-47. Xu, X., & von Davier, M. (2008). Fitting the structured general diagnostic model to NAEP data. ETS research report, RR-08-27.

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