Analysing a Quality-of-Life Survey by Using a Coclustering Model for Ordinal Data and Some Dynamic Implications

Abstract

Summary The data set that motivated this work is a psychological survey on women affected by a breast tumour. Patients replied at different stages of their treatment to questionnaires with answers on an ordinal scale. The questions relate to aspects of their life referred to as ‘dimensions’. To assist psychologists in analysing the results, it is useful to highlight the structure of the data set. The clustering method achieves this 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 ‘coclustering’. However, placing questions in the same group when they are not related to the same dimension does not make sense from a psychological perspective. Therefore, constrained coclustering was performed to prevent questions of different dimensions from being placed in the same column cluster. The evolution of coclusters over time was then investigated. The method uses a constrained latent block model embedding a probability distribution for ordinal data. Parameter estimation relies on a stochastic expectation–maximization algorithm associated with a Gibbs sampler, and the integrated completed likelihood–Bayesian information criterion is used to select the number of coclusters.

A Survey on Model-Based Co-Clustering: High Dimension and Estimation Challenges

“…The most considered missing data case is certainly the Missing At Random case (so-called MAR), where the missingness mechanism does not depend on the unobserved data values. There already exist some examples in LBM, as in [Selosse et al, 2019b, Selosse et al, 2020a, Frisch et al, 2022 and references herein. However, the Missing Not At Random case (so-called MNAR), where the missingness depends on the unobserved data values and possibly on the observed data values, is less studied both in MBC and in LBM even if some early works address this case in MBC with [Sportisse et al, 2021] and in LBM with [Corneli et al, 2020].…”

“…The BOS distribution involves a marginalization over several latent variables, resulting from the modelled data generation process. Consequently, the inference of this LBM model relies on the SEM-Gibbs algorithm (described in Section 2.4) containing an additional stage in the SE step, in which these latent variables are simulated according to the simulated value of z and w. This co-clustering model has shown his interest in applications in Psychology [Selosse et al, 2019b] and Marketing [Jacques and Biernacki, 2018]. An alternative model for ordinal data has been proposed in [Corneli et al, 2020].…”

Model-based co-clustering for mixed type data

“…Secondly, the user can consider, for practical reasons, that some features necessarily have to be separated because it does not make sense to gather them in a same column cluster. This case is not explored in the present work, but the reader can refer to [20] for a detailed example. The sets of elements (x 1 , .…”