Hierarchical marginal models with latent uncertainty

In responding to a rating question, 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 behavior may lead to misleading results, we define a multivariate model for ordinal rating responses by introducing, for every item and every respondent, a binary latent variable that discriminates aware from uncertain responses. Some independence assumptions among latent and observable variables characterize the uncertain behavior and make the model easier to interpret. Uncertain responses are modeled by specifying probability distributions that can depict different response styles. A marginal parameterization 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.