Modelling uncertainty in bivariate models for ordinal responses

We consider the case of two ratings driven by two latent variables, conditionally on one or more discrete explanatory variables. The idea is that an individual responds to each rating according to his/her knowledge (feeling) or following a random response style (uncertainty). The joint distribution of the ordinal responses results in a mixture of four components corresponding to the cases of uncertainty in both the answers, feeling in both the answers and uncertainty in only one of them. The effect of covariates can be modelled on both the marginal distributions of the ordinal variables and the association between these ordinal variables. Estimation is pursued by means of EM algorithm. Two case studies illustrate the main results.