Bias of Ability Estimates Using Warm’s Weighted Likelihood Estimator (WLE) in the Generalized Partial Credit Model (GPCM)

Summary

Application of IRT models to practical situations requires that parameter estimates be unbiased. Park & Swaminathan(1998) investigated the properties of maximum likelihood estimator(MLE) and Expected a posterior (EAP) estimators of ability parameters in the Generalized partial credit model (GPCM) and found that there was considerable bias of estimates in the GPCM under all conditions. Warm(1989) proposed the weighted likelihood estimator(WLE) for the 3-PL IRT model to reduce bias of MLE and showed that WLE produced less bias of estimates than ML and Bayesian estimation.

The purpose of this study is to apply WLE to the GPCM to reduce bias of estimates of ability parameters. In addition, this study investigates the properties of WLE, EAP, and ML estimates of ability parameters in the GPCM. The study shows that WLE considerably reduces the bias of estimates of ability parameters in the GPCM. WLE performs especially better than EAP and does similar to ML across all conditions. WL estimates performs better than ML estimate especially with small number of items (3 category 9 items). Conclusively, WLE could be applied to other polytomous IRT models in addition to GPCM to obtain unbiased estimates.