Inference on Logistic Regression Models
Abstract (Summary)The logistic regression model is one of the popular mathematical models for the analysis of binary data with applications in physical, biomedical, and behavioral sciences, among others. The feature of this model is to quantify the effects of several explanatory variables on one dichotomous outcome variable. Normally, the asymptotic properties of the maximum likelihood estimates in the model parameters are used for statistical inference. However, logistic regression models have serious numerical problems if zero cells occur in the contingency table. For this scenario, this dissertation proposed a new approach to investigate the asymptotic properties of maximum likelihood estimators for the logistic regression models. In this dissertation, a generalization of the hybrid logistic regression model was introduced, which was originally proposed by Chen et al. (2003). These models deal with situations in which risk factors associated with the outcome are exceedingly rare in the control group. In principle, a two-stage hybrid procedure models the risks due to the rare factors in the first stage and models the residual risks due to the other factors in the second stage using the standard logistic regression model. Another highlight of this dissertation is on the multinomial logistic regression model, which handles the categorical dependent outcome variable with more than two levels. It extended the hybrid logistic regression model to the multinomial hybrid logistic regression model when the case group of the outcome variable has mutually exclusive and exhaustive subgroups. In the last part of the dissertation, we studied the bootstrap method to estimate the variances for the parameter estimates in the logistic regression model.
School Location:USA - Ohio
Source Type:Master's Thesis
Date of Publication:01/01/2008