Item response model proposal under a uniform latent variable assumption: Application to school bullying data

Abstract

School bullying victimization is a variable that cannot be directly measured. Taking into account that this variable has a lower bound given by the absence of bullying victimization, we propose the use of Item Response Theory (IRT) logistic models, where the latent parameter ranges from $0$ to a positive real number $R$, adequately defining the IRT parameters and also including an empirical anchor estimation procedure. As academic abilities and school bullying victimization can be explained by associated factors such as habits, sex, socioeconomic level and education level of parents, IRT regression models are proposed to be able to perform joint inferences about individual and school characteristic effects.