Modeling Over-dispersed Binary Outcome Data

Many a time data admit more variability than expected under the assumed distribution. The greater variability than predicted by the generalized linear model random component reflects overdispersion. Overdispersion occurs because the mean and variance components of a GLM are related and depends on the same parameter that is being predicted through the independent vector. In the context of logistic regression, overdispersion occurs when the discrepancies between the observed responses and their predicted values are larger than what the binomial model would predict. The problem of overdispersion may also be confounded with the problem of omitted covariates. If overdispersion is present in a data set, the estimated standard errors and test statistics the overall goodness-of-fit will be distorted and adjustments must be made and the interpretation of the model will be incorrect and any predictions will be too imprecise. In this book, we applied Quasilikelihood techniques (Scaling), William's procedure, Generalized Estimating Equation (GEE) to real-life datasets and proved it overcome the problem of overdispersion. We employed the free statistical software R version 3.1.