Markov switching stereotype logit models for longitudinal ordinal data affected by unobserved heterogeneity in responding behavior

Abstract When asked to assess their opinion about attitudes or perceptions on Likert-scale, respondents often endorse the midpoint or extremes of the scale and agree or disagree regardless of the content. These responding behaviors are known in the psychometric literature as middle, extremes, aquiescence and disacquiescence response styles that generally introduce bias in the results. One of the key motivations behind our approach is to account for these attitudes and how they evolve over time. The novelty of our proposal, in the context of longitudinal ordered categorical data, is in considering simultaneously the temporal dynamics of the responses (observable ordinal variables) and unobservable answering behaviors, possibly influenced by response styles, through a Markov switching logit model with two latent components. One component accommodates serial dependence and respondent’s unobserved heterogeneity, the other component determines the responding attitude (due to response styles or not). The dependence of the responses on covariates is modelled by a stereotype logit model with parameters varying according to the two latent components. The stereotype logit model is adopted because it is a flexible extension of the proportional odds logit model that retains the advantage of using a single parameter to describe a regressor effect. In the paper, a new interpretation of the parameters of the stereotype model is given by defining the allocation sets as intervals of values of the linear predictor that identify the most probable response. Unobserved heterogeneity, serial dependence and tendency to response style are modelled through our approach on longitudinal data, collected by the Bank of Italy.