Individual random effects model for differences in trait distribution among respondents.

The homogeneity hypothesis is a common assumption in classic measurement. However, the item response theory model assumes that different respondents with same ability have the same option probabilities, which may not hold. The aim of this study is to propose a new individual random effect model that accounts for the differences in option probabilities among respondents with same latent traits by using within-person variance. The performance of the new model is evaluated through simulation studies and real data using the PRESUPP scale of PISA. The model parameters are estimated by the MCMC method. The results show that the individual random effect model can provide more accurate parameter estimates and obtain a scale parameter to describe the distribution of respondents' abilities, under different within-person variances. The new model has lower RMSE and better model fit than the classic IRT model.