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

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.

Asymptotic Variance of Linking Coefficient Estimators for Polytomous IRT Models

In item response theory (IRT), when two groups from different populations take two separate tests, there is a need to link the two ability scales so that the item parameters of the tests are comparable across the groups. To link the two scales, information from common items are utilized to estimate linking coefficients which place the item parameters on the same scale. For polytomous IRT models, the Haebara and Stocking–Lord methods for estimating the linking coefficients have commonly been recommended. However, estimates of the variance for these methods are not available in the literature. In this article, the asymptotic variance of linking coefficients for polytomous IRT models with the Haebara and Stocking–Lord methods are derived. The results are presented in a general form and specific results are given for the generalized partial credit model. Simulations which investigate the accuracy of the derivations under various settings of model complexity and sample size are provided, showing that the derivations are accurate under the conditions considered and that the Haebara and Stocking–Lord methods have superior performance to several moment methods with performance close to that of concurrent calibration.