Title: “A Multivariate Mixture Model for Responses to Rating Questions allowing for Uncertainty”

Abstract:

This talk proposes a multivariate model for ordinal rating responses, allowing for uncertainty in answering. In responding to rating questions, an individual may give answers either according to his/her knowledge (feeling) or to his/her level of indecision (uncertainty). Since ignoring this uncertainty may lead to misleading results, we define the joint distribution of the ordinal responses via a mixture of components, characterized by uncertainty in answering to a subset of variables. A marginal approach is proposed to parameterize the models and the effectiveness of the model is attested through an application to real data and supported by a Monte Carlo study.

Uncertain people can be assumed to give an answer at random, by assigning equal probability to every category in the scale (Uniform distribution), but in most cases, wavering respondents tend to use only a small number of the available rating scale options: someone may skip extreme values, optimists may overvalue their feelings and pessimists may underrate them, someone else can take shelter in the middle category. The proposed approach aims to model adequately the distribution of responses, given with uncertainty, according to these different behaviors, by U-shaped, bell shaped, symmetric and skewed distributions. Moreover, since the proposed models are based on some restrictive assumptions which assure identifiability, the true distribution is not necessarily in the model we are using. For this reason, testing procedures for comparing competitive models will be dealt with by avoiding the assumption of correct specification of the models.