Statistical analysis of questionnaire data is often performed employing techniques from item-response theory. In this framework, it is possible to differentiate respondent profiles and characterize the questions (items) included in the questionnaire via interpretable parameters. These models are often crosssectional and aim at evaluating the performance of the respondents. The motivating application of this work is the analysis of psychometric questionnaires taken by a group of mothers at different time points and by their children at one later time point. The data are available through the GUSTO cohort study. To this end, we propose a Bayesian semiparametric model and extend the current literature by: (i) introducing temporal dependence among questionnaires taken at different time points; (ii) jointly modeling the responses to questionnaires taken from different, but related, groups of subjects (in our case mothers and children), introducing a further dependency structure and therefore sharing of information; (iii) allowing clustering of subjects based on their latent response profile. The proposed model is able to identify three main groups of mother/child pairs characterized by their response profiles. Furthermore, we report an interesting maternal reporting bias effect strongly affecting the clustering structure of the mother/child dyads.
Keywords: Dirichlet process; clustering; cohort study; item-response theory; questionnaire data.
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