  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.
