  In social sciences, studies are often based on questionnaires asking
participants to express ordered responses several times over a study period. We
present a model-based clustering algorithm for such longitudinal ordinal data.
Assuming that an ordinal variable is the discretization of a underlying latent
continuous variable, the model relies on a mixture of matrix-variate normal
distributions, accounting simultaneously for within- and between-time
dependence structures. The model is thus able to concurrently model the
heterogeneity, the association among the responses and the temporal dependence
structure. An EM algorithm is developed and presented for parameters
estimation. An evaluation of the model through synthetic data shows its
estimation abilities and its advantages when compared to competitors. A
real-world application concerning changes in eating behaviours during the
Covid-19 pandemic period in France will be presented.
