Formulation and application of the generalized multilevel facets model

In this study, the authors develop a generalized multilevel facets model, which is not only a multilevel and two-parameter generalization of the facets model, but also a multilevel and facet generalization of the generalized partial credit model. Because the new model is formulated within a framework of nonlinear mixed models, no efforts are needed to develop parameter estimation procedures, and existing computer programs can be directly applied. Through simulations, the authors found that the parameters in the generalized multilevel facets model could be recovered fairly well using the SAS NLMIXED procedure. To illustrate applications of the new model, a real data set about ratings of household appliances was analyzed with gender, age, and education level as the Level 2 predictors. Further model generalization is discussed.