Extra-Binomial Variation in Logistic Linear Models

Abstract

Summary The logistic‐linear model, and its maximum likelihood estimation by iterated reweighted least squares, can be simply modified to incorporate a component of extra‐binomial variation. The modifications are very easily effected if the GLIM program is used.

The Edinburgh randomised trial of breast cancer screening: results after 10 years of follow-up

“…Rates in study and control pract were compared and their ratio alculated. As before (Roberts et al, 1990), a modified logistic regrsion procedure incorporated adjustment for extrabinomial regression (Williams, 1982) so as to respect the cluster randomisation. All analyses were implemented in 'GLIM' and stratified by age at survey entry (45-49, 50-54, 55-59 and 60-64 years).…”

Reproductive Biology of Fidiobia dominica (Hymenoptera: Platygastridae), an Egg Parasitoid of Diaprepes abbreviatus (Coleoptera: Curculionidae)

“…We used a GLM with a binomial error distribution to analyze the relationship between the percentage of eggs fertilized and the mating treatment. To correct for overdispersion, we used the Williams (1982) method. Female body size and the night that eggs were laid also were included in both analyses.…”

A comparative study of models for correlated binary data with applications to health services research

“…The methods range from a simple rescaling of the covariance matrix by a single inflator factor to a full likelihood based inference. To mention few, Williams (1975) first proposed the use of betabinomial model and later proposed fitting weighted logistic regression (Williams, 1982). More recently, the generalized estimating equation was proposed by Liang and Zeger (1986) in regression analysis of repeated measurement.…”