Performance of Polytomous IRT Models With Rating Scale Data: An Investigation Over Sample Size, Instrument Length, and Missing Data

Abstract

The implementation of polytomous item response theory (IRT) models such as the graded response model (GRM) and the generalized partial credit model (GPCM) to inform instrument design and validation has been increasing across social and educational contexts where rating scales are usually used. The performance of such models has not been fully investigated and compared across conditions with common survey-specific characteristics such as short test length, small sample size, and data missingness. The purpose of the current simulation study is to inform the literature and guide the implementation of GRM and GPCM under these conditions. For item parameter estimations, results suggest a sample size of at least 300 and/or an instrument length of at least five items for both models. The performance of GPCM is stable across instrument lengths while that of GRM improves notably as the instrument length increases. For person parameters, GRM reveals more accurate estimates when the proportion of missing data is small, whereas GPCM is favored in the presence of a large amount of missingness. Further, it is not recommended to compare GRM and GPCM based on test information. Relative model fit indices (AIC, BIC, LL) might not be powerful when the sample size is less than 300 and the length is less than 5. Synthesis of the patterns of the results, as well as recommendations for the implementation of polytomous IRT models, are presented and discussed.