An aspect of discrete data analysis: fitting a beta-binomial distribution to the hospitals' data.

Abstract

Statistical analysis for discrete data, particularly for probability models such as the binomial, Poisson and multinomial, is by now very well understood, with a wealth of suitable software. It can happen that the standard generalized linear modelling (glm) software is not completely appropriate, since over-dispersion is present, relative to the standard distributions such as the Poisson or the binomial. Failure to take account of this over-dispersion, for example in fitting a model such as log(p/(1 - p)) = alpha + beta x (where the covariate x is the dose) will mean that our estimates of beta will be less precise than the binomial-based formula gives us. Thus for example we will be quoting confidence intervals for beta that are too narrow. One way of coping with this problem is to use a probability model which is more general than the binomial, and one such model is the beta-binomial. This paper discusses beta-binomial modelling (in S-Plus) in relation to the interesting data set given in the 1998 BMJ paper by Spiegelhalter and Marshall on success rates of 52 in vitro fertilisation clinics in the UK.

Cite this paper

@article{Altham2002AnAO, title={An aspect of discrete data analysis: fitting a beta-binomial distribution to the hospitals' data.}, author={P . M . E . Altham}, journal={Developments in biologicals}, year={2002}, volume={107}, pages={77-83} }