Modelling Ordinal Responses with Uncertainty: a Hierarchical Marginal Model with Latent Uncertainty components

Abstract: In responding to rating questions, an individual may give answers either according to his/her knowledge/awareness or to his/her level of indecision/uncertainty, typically driven by a response style. As ignoring this dual behaviour may lead to misleading results, we define a multivariate model for ordinal rating responses, by introducing, for every item, a binary latent variable that discriminates aware from uncertain responses. Some independence assumptions among latent and observable variables characterize the uncertain behaviour and make the model easier to interpret. Uncertain responses are modelled by specifying probability distributions that can depict different response styles characterizing the uncertain raters. A marginal parametrization allows a simple and direct interpretation of the parameters in terms of association among aware responses and their dependence on explanatory factors. The effectiveness of the proposed model is attested through an application to real data and supported by a Monte Carlo study.