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Multi-level zero-inflated Poisson regression modelling of correlated count data with excess zeros

Department of Epidemiology and Biostatistics, School of Public Health, Curtin University of Technology, Perth, WA, Australia, Andy.Lee{at}curtin.edu.au

Kui Wang

Department of Epidemiology and Biostatistics, School of Public Health, Curtin University of Technology, Perth, WA, Australia

Jane A. Scott

Division of Developmental Medicine, University of Glasgow, UK

Kelvin K.W. Yau

Department of Management Sciences, City University of Hong Kong, Hong Kong

Geoffrey J. McLachlan

Department of Mathematics, University of Queensland, Brisbane, Qld., Australia

Count data with excess zeros relative to a Poisson distribution are common in many biomedical applications. A popular approach to the analysis of such data is to use a zero-inflated Poisson (ZIP) regression model. Often, because of the hierarchical study design or the data collection procedure, zero-inflation and lack of independence may occur simultaneously, which render the standard ZIP model inadequate. To account for the preponderance of zero counts and the inherent correlation of observations, a class of multi-level ZIP regression model with random effects is presented. Model fitting is facilitated using an expectation-maximization algorithm, whereas variance components are estimated via residual maximum likelihood estimating equations. A score test for zero-inflation is also presented. The multi-level ZIP model is then generalized to cope with a more complex correlation structure. Application to the analysis of correlated count data from a longitudinal infant feeding study illustrates the usefulness of the approach.

Statistical Methods in Medical Research, Vol. 15, No. 1, 47-61 (2006)
DOI: 10.1191/0962280206sm429oa


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