Model fit criteria curve behaviour in class enumeration - a diagnostic tool for model (mis)specification in longitudinal mixture modelling

The use of longitudinal finite mixture models (FMMs) to identify latent classes of individuals following similar paths of temporal development is gaining traction in applied research. However, FMM's users may be unaware of how data features as well as the inappropriate specification of the model's covariance structure impacts class enumeration. To elucidate this, we investigated model fit-criteria curve behaviour across an array of data conditions and covariance structures. Fit statistic patterns were variable among the fit criteria and across a range of data conditions. This variability was greatly attributable to the level of class separation and the presence/absence of random effects. Our findings support some widely held notions (e.g. BIC outperforms other criteria) while debunking others (adding random effects is not always the solution). Based on the obtained results, we present guidelines on how the behaviour of fit criteria curves can be used as a diagnostic aid during class enumeration.