Retrofitting of Polytomous Cognitive Diagnosis and Multidimensional Item Response Theory Models

Abstract

In this study, person parameter recoveries are investigated by retrofitting polytomous attribute cognitive diagnosis and multidimensional item response theory (MIRT) models. The data are generated using two cognitive diagnosis models (i.e., pG-DINA: the polytomous generalized deterministic inputs, noisy “and” gate and fA-M: the fully-additive model) and one MIRT model (i.e., the compensatory two-parameter logistic model). Twenty-five replications are used for each of the 54 conditions resulting from varying the item discrimination index, ratio of simple to complex items, test length, and correlations between skills. The findings are obtained by comparing the person parameter estimates of all three models to the actual parameters used in the data generation. According to the findings, the most accurate estimates are obtained when the fitted models correspond to the generating models. Comparable results are obtained when the fA-M is retrofitted to other data or when the MIRT model is retrofitted to fA-M data. However, the results are poor when the pG-DINA is retrofitted to other data or the MIRT is retrofitted to pG-DINA data. Among the conditions used in the study, test length and item discrimination have the greatest influence on the person parameter estimation accuracy. Variation in the simple to complex item ratio has a notable influence when the MIRT model is used. Although the impact on the person parameter estimation accuracy of the correlation between skills is limited, its effect on MIRT data is more significant.