| Overdispersion is the presence of greater variability in a data set than one would expect based on a given simple statistical model. When the observed variance is higher than the anticipated variance of an assumed theoretical model, then it may be an indication of overdispersion. When there is such a suspicion, the natural reaction would be to test whether there are valid reasons to assume the same. In many cases, the overdispersion parameter is incorporated to the model with an introduction of random effects. Throughout this thesis, it is assumed that the primary data are coming from a binomial distribution and hence the testing is for extra-binomial variation.;For testing overdispersion, instead of a score test statistic derived from likelihood functions, a quasi-score test statistic is developed based on quasi-likelihood functions. A simulation study is carried out to explore the performance of the quasi-score test for testing overdispersion in binomial regression.;Subsequent to any evidence of an overdispersion in the data set, this parameter together with the regression parameters are estimated using quasi-likelihood methods. The marginal moments used in the quasi-likelihood functions are obtained using two different approaches. Simulations are carried out to study the finite-sample properties of the estimators under correctly specified and misspecified random effects. Thereby, bias, root mean squared error, and coverage probability and mean length of 95% confidence intervals are obtained. |
