The Problem Of Overdispersion In Logistic Regression

Abstract

Overdispersion is caused by the variability of the response probability or correlatioti between the bitiary responses. The aim of this research is coniparing the parameter estiliiate from Logistic Regression (LR), Willialiis Method (WM), atid Beta-Binomial Regression (BBR). From tlie value of tlie pearson chi-square and deviance, the logistic regression of acadeliiic achievement exhibit overdispersion. The parameter estimate of LR, WM, and BBR are not significant different visually. The difference is seen obviously from tlie value of standard error. The value of standard error from WM and BBR are greater than LR. It's as a conseqoently of overdispersion. In other word, tlie standard error from LR doesn't accolllrnodate tlie problem, causing the valrte of standard error from LR is underestimate. Based on tlie result of analyse, tlie GPA TPB call be seen as an indicator ofacade~nica cliievement in the next level. Based on tlie result of simulation, it is tested parameter estitnate and standard error from some cases of correlation between the binary responses (overdispersion) for the three methods. As a result, When there is no overdispersion, tlie parameter estimate and the stantlard error from the three methods are not significant different. When tliere is overdispersion, the parameter estimate from LR, WM, and BBR are not signilica~itl ii%crcnt, but thc valuc oI"stantli~~-c(1rr or from WM ;~ndB BR arc grcatcr tlia~iL R. Tlie valuc of standard error fiom LR is relitlively similar ibr all of the cases, while the value ofstandard error from WM and BBR increase as the correlation raises.