Multi-way comparisons and generalized linear models of nest success: extensions of the Mayfield method

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Abstract
The Mayfield method of estimating a constant probability of daily nest success adjusts for the fact that nests found part-way through a nesting stage (egglaying, incubation or brood-rearing) have, by definition, not failed since the stage began. The equality of two independently estimated probabilities can be tested using their associated standard errors. However, published Mayfield methodology does not extend to testing the equality of three or more probabilities, considering multi-way comparisons, or fitting complex regression-type models. It is important that such flexibility is accessible to biologists. I present an overview of the statistical model underlying the Mayfield method and of its assumptions, and present a test of goodness-of-fit based on the deviance. The model is extended to one-way classifications numbering two or more categories. A hypothesis test of the equality of all category-specific probabilities is derived based on the likelihood-ratio statistic. Relevant formulae are given explicitly to enable calculations to be done without computer software. More complex models can be fitted and compared within the framework of generalized linear modelling, noting that logistic regression produces deviances, parameter estimates and asymptotic variances that are identical to those obtained from matching Mayfield models. The estimation and hypothesis-testing procedures are illustrated using British Trust for Ornithology Nest Record Scheme data for the Corn Bunting and the Song Thrush.