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Unformatted text preview: Analysis of the human sex ratio by using overdispersion models J. K. Lindsey { Limburgs Universitair Centrum, Diepenbeek, Belgium and P. M. E. Altham University of Cambridge, UK [Received December 1996. Final revision April 1997] Summary. For study of the human sex ratio, one of the most important data sets was collected in Saxony in the 19th century by Geissler. The data contain the sizes of families, with the sex of all children, at the time of registration of the birth of a child. These data are reanalysed to determine how the probability for each sex changes with family size. Three models for overdispersion are fitted: the beta–binomial model of Skellam, the ‘multiplicative’ binomial model of Altham and the doublebinomial model of Efron. For each distribution, both the probability and the dispersion parameters are allowed to vary simultaneously with family size according to two separate regression equations. A finite mixture model is also fitted. The models are fitted using nonlinear Poisson regres sion. They are compared using direct likelihood methods based on the Akaike information criterion. The multiplicative and beta–binomial models provide similar fits, substantially better than that of the doublebinomial model. All models show that both the probability that the child is a boy and the dispersion are greater in larger families. There is also some indication that a point probability mass is needed for families containing children uniquely of one sex. Keywords : Akaike information criterion; Beta–binomial distribution; Direct likelihood inference; Doublebinomial distribution; Finite mixture model; ‘Multiplicative’ binomial distribution; Nonlinear...
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