Abstract

Polytomous item responses are prevalent in background or context questionnaires of International large-scale assessments (ILSA). Responses to these types of instruments can vary in their symmetry or skewness. Zero inflation of responses can lead to biased estimates of item parameters in the response model and also to a downward bias in the conditional model when the zero inflated component is not accounted for in the model. In this paper, we propose to use a mixture continuation ratio response model to approximate the non-normality of the latent variable distribution. We use responses to bullying items from an ILSA study, which typically present positive asymmetry. The present model allows us to distinguish bullying victimization risk profiles among students, retrieve bullying victimization risk scores, and determine the population prevalence of the bullying events. This study also aims to illustrate how to fit a mixture continuation ratio model, including complex sampling design, thus expanding the modeling tools available for secondary users of large-scale assessment studies.