An adjusted scale binomial Beta H-Likelihood estimation method for unbalanced clustered binary response models

Abstract

In practice, clustered binary responses are very prevalent, where binary data is naturally grouped by sampling techniques. Clusters are often unequal in size in some areas of studies, such as medicine, education and others. The most suitable models for binary data clusters of unbalanced sizes are the Hierarchical Generalized Linear Model (HGLM), where the random term over-dispersion counts; and it is k known as clustered binary data. Current techniques for estimating parameters in (HGLM) are many, but these techniques do not allow over dispersion to be distinct from cluster to cluster. Where clustered binary data resulted in over-variation, that reasonable to conclude the unequal size of clustered binary data may have been distinct variations for distinct clusters. By ignoring the chance of shifting over variability between clusters, test statistics may be inflated in the Type I error rates. In this paper, the binomial beta (BB) (HGLM) method has been altered to account for distinct variations across separate clusters. In order to explore whether the Adjusted Scale Binomial Beta (ASBB) method is more suitable than the (BB) technique for dealing with over-dispersion for unequal cluster binary data models, the author was used simulation, the adjusted method was compared to the original "existing" technique in terms of, Type I error rate, estimator standard errors and power. (ASBB) h-likelihood “adjusted” method was comparable to BB "existing" technique, as it has a less standard error and the Type I error was acceptable. Moreover, Type I error inflated in “exist method” (BB) h-likelihood.