Models for overdispersed, correlated count entomological data

Abstract

Outcomes of interest for entomological data are often in the form of counts and as a first step, a standard model to analyse this type of data is the Poisson model, an example of generalized linear models. The basic model assumptions are independence of observations and constant rate of event occurrence. If one or both of these assumptions failure the variance of the data will be greater (smaller) than the variance expected using the Poisson model resulting in what is called overdispersion (undersispersion). Many different models for overdispersion (underdispersion) can arise from alternative possible mechanisms for the underlying process. Another reason for extending the Poisson model is because of the occurrence of a hierarchical structure in the data caused by a clustering resulted from repeatedly measuring the outcome on the same experimental unit. In entomological applications involving count data there is often an excess of zero observations. In this work we present a review of models that can be used to take into account the different aspects of the failure of the Poisson model assumptions. The proposed methodology is illustrated using data of an experiment to evaluate 25 isolates of entomopathogenic fungi (Metarhizium spp., B. bassiana and I. fumosorosea) and compare with the three reference treatments on the control of T. urticae. We compared the results and also discussed model selection and diagnostics. For grouping the isolates we proposed two different methods. All the methods were implemented in the software R.