Mixture models for eye-tracking data: a case study.
Heterogeneity in biomedical data is often a source of great scientific interest and mixture models provide a general framework for modelling the various types that arise in practice. Finite mixture models model discrete subgroups within populations while continuous mixture models inflate the variance to account for over-dispersed data. A potential problem with the application of finite mixture models in practice is that these models may drastically overestimate the number of component densities when there is a lack of model fit. This can have severe consequences, leading the data analyst to attach substantive interpretations to spurious subgroups. For this reason, we propose using the continuous mixture model as an alternative when fitting finite mixture models with an arbitrary number of components. In the context of an example examining a specific oculomotor component of eye-tracking dysfunction in schizophrenia, we demonstrate why the continuous mixture model provides a viable alternative to the finite mixture model for small sample sizes. We present methods for fitting and comparing both models using the parametric bootstrap and EM algorithm, and show that the distinction between the models decreases as the number of component densities in the finite mixture model increases.