Traditional cluster analysis methods are not based on likelihoods and thus the toolbox of statistical inference can’t be used for them. For instance, goodness of fit can’t be assessed using well-developed criteria such as the AIC. Following the lines of Pledger and Arnold 2013, we develop likelihood-based probability models to cluster ordinal data that arises in longitudinal settings.
In this talk, we present the Trends Odds Model (TOM) that includes mixture-based fuzzy clustering to identify similar groups. The estimation procedure is carried out using the EM algorithm. We also illustrate our models using survey data from the Household, Income and Labour Dynamics in Australia (HILDA). In particular, we examine self-reported health status (poor, fair, good, very good and excellent) from the 2001-2010 waves.