Analyzing rating distributions with heaps and censoring points using the generalized Craggit model

Abstract

In this article, we introduce a new, highly flexible model to analyze distributions with heaps and censoring points, which we call the generalized Craggit model. Distributions with heaps and censoring points can be found in many social science applications. For example, such distributions can be the result of sequential or multistep rating processes. Our model is a combination of a Craggit model and a generalized ordered probit model. It can account for multiple heaps and censoring points in distributions. We used this model to analyze a factorial survey experiment on earnings justice attitudes in the SOEP-Pretest 2008. In this experiment, a three-step rating instrument was used, which resulted in a rating distribution with heaps and censoring. Our generalized Craggit model fits the data of this experiment much better than a hierarchical linear model, which is the method that is usually implemented to analyze factorial survey experiments.