The Random-Effect Generalized Rating Scale Model

Rating scale items have been widely used in educational and psychological tests. These items require people to make subjective judgments, and these subjective judgments usually involve randomness. To account for this randomness, Wang, Wilson, and Shih proposed the random-effect rating scale model in which the threshold parameters are treated as random effects rather than fixed effects. In the present study, the Wang et al. model was further extended to incorporate slope parameters and embed the new model within the framework of multilevel nonlinear mixed-effect models. This was done so that (1) no efforts are needed to derive parameter estimation procedures, and (2) existing computer programs can be applied directly. A brief simulation study was conducted to ascertain parameter recovery using the SAS NLMIXED procedure. An empirical example regarding students interest in learning science is presented to demonstrate the implications and applications of the new model.