A random item effects generalized partial credit model with a multiple imputation-based scoring procedure.

Purpose: Random item effects item response theory (IRT) models have received much attention for more than a decade. However, more research is needed on random item effects IRT models for polytomous data. Additionally, to improve the utility of this new class of IRT models, the scoring issue must be addressed.

Methods: We proposed a new random item effects generalized partial credit model (GPCM), which considers both random person and random item and category-specific effects. In addition, we introduced a multiple imputation (MI)-based scoring procedure that applies to various random item effects IRT models. To evaluate the proposed model and scoring procedure, we analyzed data from a Quality of Life (QoL) scale for the Chronically Mentally III and conducted a preliminary simulation study.

Results: In the empirical data analysis, we found that patient scores generated based on the proposed model and scoring procedure were almost identical to those obtained through the conventional GPCM and scoring method. However, the standard errors (SEs) associated with the scores were slightly larger when the proposed approach was utilized. In the simulation study, we observed adequate recovery of the model parameters and patient scores.

Conclusion: The proposed model and MI-based scoring procedure contribute to the literature. The proposed model substantially reduces the number of free parameters in comparison to a conventional GPCM, which can be desired when sample sizes are small, e.g., special populations. In addition, the MI-based scoring procedure addresses the scoring issue and can be easily extended for scoring with other random item effects IRT models.