Yousri Slaoui - Mixture of longitudinal factor analyzers with application to chronic pain

Multivariate longitudinal data are used in a variety of
research areas not only because they allow to analyze time
trajectories of multiple indicators, but also to determine how these
trajectories are influenced by other covariates. In this article, we
propose a mixture of longitudinal factor analyzers. This model could
be used to extract latent factors representing multiple longitudinal
noisy indicators in heterogeneous longitudinal data and to study the
impact of one or several covariates on these latent factors. One of
the advantages of this model is that it allows for measurement
non-invariance, which arises in practice when the factor structure
varies between groups of individuals due to cultural or physiological
differences. This is achieved by estimating different factor models
for different latent classes. The proposed model could also be used to
extract latent classes with different latent factor trajectories over
time. Other advantages of the model include its ability to take into
account heteroscedasticity of errors in the factor analysis model by
estimating different error variances for different latent classes. We
first define the mixture of longitudinal factor analyzers and its
parameters. Then, we propose an EM algorithm to estimate these
parameters. We propose a Bayesian information criterion to identify
both the number of components in the mixture and the number of latent
factors. We then discuss the comparability of the latent factors
obtained between subjects in different latent groups. Finally, we
apply the model to simulated and real data of patients with chronic
postoperative pain.