Dose Response Models with Natural Mortality and Random Effects
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- Urbano, M.R., Hinde, J. & Demétrio, C.G.B. JABES (2013) 18: 594. doi:10.1007/s13253-013-0150-1
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When fitting dose–response models to entomological data it is often necessary to take account of natural mortality and/or overdispersion. The standard approach to handle natural mortality is to use Abbott’s formula, which allows for a constant underlying mortality rate. Commonly used overdispersion models include the beta-binomial model, logistic-normal, and discrete mixtures. Here we extend the standard natural mortality model by including a random effect to account for overdispersion. Parameter estimation is based on a combined EM Newton–Raphson algorithm, which provides a simple framework for maximum likelihood estimation of the natural mortality model. We consider the application of this model to data from an experiment on the use of a virus (PhopGV) for the biological control of worm larvae (Phthorimaea operculella) in potatoes. For this natural mortality model with a random effect we introduce the likelihood ratio test, effective dose, and the use of a simulated residual envelope for model checking. Comparisons are made with an equivalent beta-binomial model. The procedures are implemented in the R system.