Overdispersed Logistic Regression Model

When binary data are obtained through simple random sampling, the covariance for the responses follows the binomial model (two possible outcomes from independent observations with constant probability). However, when the data are obtained under other circumstances, the covariances of the responses differ substantially from the binomial independent outcomes. For example, clustering effects or subject effects in repeated measure experiments cause the variance of the observed proportions to be much larger than the variances if observed under the binomial assumption. The phenomenon is generally referred to as overdispersion or extra variation. The presence of overdispersion affects the standard errors and, therefore, also affects the conclusions made about the significance of the predictors. This chapter presents a method of analysis based on work presented in the following: