Bayesian model-based clustering for longitudinal ordinal data

Abstract

Traditional cluster analysis methods used in ordinal data, for instance k-means and hierarchical clustering, are mostly heuristic and lack statistical inference tools to compare among competing models. To address this we propose a latent transitional model, a finite mixture model that includes both observed and latent covariates and apply it for the first time to the case of longitudinal ordinal data. This model-based clustering model is an extension of the proportional odds model and includes a first-order transitional term, occasion effects and interactions which provide flexible ways to capture different time patterns by cluster as well as time-heterogeneous transitions. We estimate model parameters within a Bayesian setting using a Markov chain Monte Carlo scheme and block-wise Metropolis–Hastings sampling. We illustrate the model using 2001–2011 self-reported health status (SRHS) from the Household, Income and Labour Dynamics in Australia survey. SRHS is recorded as an ordinal variable with five levels: poor, fair, good, very good and excellent. Using the Widely Applicable Information Criterion for model comparison, we find evidence for six latent groups. Transitions in the original data and the estimated groups are visualized using heatmaps.