Analysis Of Bias-Corrected And Exact Estimators For Binomial Generalized Linear Model Parameters

Typically, small samples have always been a problem for binomial generalized linear models. Though generalized linear models are widely popular in public health, social sciences etc. In small sample scenarios the non-existence of the maximum likelihood (ML) estimators is very common as well as separation occurs in the data. In logistic regression the maximum likelihood estimates are found to have biased away from origin. My work examines the bias-reduced and exact estimators that have been used to estimate the slope parameters and standard errors of the estimated slope parameters as compared to the traditional ML method. The present work is noted for the logistic regression. For the models having categorical responses, bias-reduction performs the best. The latest research and methodological interest in the bias-reduction technique stimulate this current work and the main goal is to evaluate and broaden the application of this approach so it would identify the areas where bias-reduction can be helpful. This research is an effort to prove theoretically and practically that bias-reduced method should be considered as an improvement over the traditional ML method. This method not only removes the first order bias in the ML method but also equivalent to the penalization of the likelihood by Jeffreys prior. Moreover, bias-reduced estimates are always find to be finite