Modelling and predicting clustered count data with excess zeros

Joint work with J. Mills Flemming (Dalhousie, Halifax) and A. Welsh (ANU, Canberra)

Clustered count data with many zero observations are typical of endangered species, particularly in marine environments, but are difficult to model with available methods. We present a general formulation for mixed effects hurdle models. A novel approach to the introduction of the random effects allows extensions beyond the usual multivariate normality assumption and facilitates inference about dependence between the two parts of the model. We obtain the fixed effects parameter estimates by maximum likelihood and develop empirical best predictors of the random effects and other cluster specific targets. We also address the unsolved issue of computing the mean squared error of these predictions. We pay careful attention to computational aspects, and use, for example, a fast bootstrap procedure. The methods are demonstrated using real data on critically endangered hammerhead sharks and evaluated with a simulation study. Our approach is more generally applicable than the hurdle model and so can be easily extended to GLMM, for example.