Dose Response Models with Natural Mortality and Random Effects |
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Authors: | M R Urbano J Hinde C G B Demétrio |
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Institution: | 1. CCE—Departamento de Estatística, Universidade Estadual de Londrina, Londrina, Paraná, Brazil 2. National University of Ireland, Galway, Ireland 3. Departamento de Ciências Exatas, Escola Superior de Agricultura “Luiz de Queiroz”, Piracicaba, S?o Paulo, Brazil
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Abstract: | 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. |
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