Analyzing quality of life survey using constrained co-clustering model for ordinal data and some dynamic implication

The dataset which motivated this work is a psychological survey on women affected by a breast tumor. Patients replied at different moments of their treatment to questionnaires with answers on ordinal scale. The questions relate to aspects of their life called dimensions. To assist the psychologists in analyzing the results, it is useful to emphasize a structure in the dataset. The clustering method achieves that by creating groups of individuals that are depicted by a representative of the group. From a psychological position , it is also useful to observe how questions may be clustered. The simultaneous clustering of both patients and questions is called co-clustering. However, getting questions into a same group when they are not related to the same dimension does not make sense from a psychologist stance. Therefore, a constrained co-clustering has been performed to prevent questions from different dimensions from getting assembled in a same column-cluster. Then, evolution of co-clusters along time has been investigated. The method relies on a constrained Latent Block Model embedding a probability distribution for ordinal data. Parameter estimation relies on a Stochastic EM-algorithm associated to a Gibbs sampler, and the ICL-BIC criterion is used for selecting the numbers of co-clusters.