Regression Methods for Overdispersed Dichotomous Response Data

Kim, Dong Kee; Han, Mooyoung; Jeon, Wootaek; Myoung, Sung Min; Song, Ki Jun

Abstract

In neuropsychiatrical research, many problems of statistical inference concern the relationship between the PTSD and traumatic experiences. The logistic model is widely used for modeling a relationship between the covariate and the magnitude of the PTSD. A common complication in the logistic model for dichotomous response data is overdispersion. In this study, two different methods for analyzing dichotomous response data are illustrated and compared. One method is the logistic regression approach, where the numbers of dichotomous responses are predicted by the logistic function of covariates. The other one is the overdispersed logistic regression approach, where the overdispersion is measured by a scale parameter in the variance function of the dichotomous response. In dichotomous response model, when reponses are overdispersed, the overdispersed logistic regression produces more appropriate standard errors of the regression coefficients and the 95% confidence intervals of odds ratios. Therefore, in neuropsychiatrical research, it is recommended to examine the overdispersion problems for their data set before applying the logistic regression model.