The effect of random-effects misspecification on classification accuracy

Mixed models are a useful way of analysing longitudinal data. Random effects terms allow modelling of patient specific deviations from the overall trend over time. Correlation between repeated measurements are captured by specifying a joint distribution for all random effects in a model. Typically, this joint distribution is assumed to be a multivariate normal distribution. For Gaussian outcomes misspecification of the random effects distribution usually has little impact. However, when the outcome is discrete (e.g. counts or binary outcomes) generalised linear mixed models (GLMMs) are used to analyse longitudinal trends. Opinion is divided about how robust GLMMs are to misspecification of the random effects. Previous work explored the impact of random effects misspecification on the bias of model parameters in single outcome GLMMs. Accepting that these model parameters may be biased, we investigate whether this affects our ability to classify patients into clinical groups using a longitudinal discriminant analysis. We also consider multiple outcomes, which can significantly increase the dimensions of the random effects distribution when modelled simultaneously. We show that when there is severe departure from normality, more flexible mixture distributions can give better classification accuracy. However, in many cases, wrongly assuming a single multivariate normal distribution has little impact on classification accuracy.