Hierarchical Models for the Analysis of Likert Scales in Regression and Item Response Analysis

Abstract

Appropriate modelling of Likert-type items should account for the scale level and the specific role of the neutral middle category, which is present in most Likert-type items that are in common use. Powerful hierarchical models that account for both aspects are proposed. To avoid biased estimates, the models separate the neutral category when modelling the effects of explanatory variables on the outcome. The main model that is propagated uses binary response models as building blocks in a hierarchical way. It has the advantage that it can be easily extended to include response style effects and non-linear smooth effects of explanatory variables. By simple transformation of the data, available software for binary response variables can be used to fit the model. The proposed hierarchical model can be used to investigate the effects of covariates on single Likert-type items and also for the analysis of a combination of items. For both cases, estimation tools are provided. The usefulness of the approach is illustrated by applying the methodology to a large data set.