Optimal Predictions in Mixed-Effects Hurdle Models

• Activity Number: 422
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Eva Cantoni*+ and Joanna Mills Flemming and Alan Welsh
• Companies: Dpt of Economics, University of Geneva and Dpt. Of Mathematics, Dalhousie University and Centre for Mathematics and its Applications, Australian National University
• Keywords: extra zeros ; optimal prediction ; Random effects hurdle models

Abstract

Clustered count data with large proportion of zeros are typical in marine species conservation. The particular structure of this response variable rules out simple models, e.g. negative binomial GLMM and independent hurdle mixed models. We provide a novel and general specification of a mixed effects hurdle regression model, where the random effects structures of the two parts of the model are dependent. In addition, we derive the optimal predictors of the random effects themselves and other cluster specific quantities, e.g. the probability of presence or the abundance given presence for a particular cluster. The variability of these predictions is assessed via a fast bootstrap procedure, such that, for example, confidence intervals of the prediction can be constructed. Our work has been motivated and is illustrated by a dataset on critically endangered hammerhead sharks, where the counts are taken on trips during which there are several hauls. For each haul of each trip the recorded covariates include information about the time, about weather conditions and about the procedure. Our approach is more generally applicable and so can be easily extended to GLMM, for example.