Date of Award
1994
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Abstract
In this dissertation, five topics related to the process and prediction of forward stepwise logistic regression are investigated.;Forward stepwise logistic regression is involved with selection and stopping criteria. Seven selection criteria are used: the likelihood ratio statistic, Lawless and Singhal (1978)'s statistic, the Wald statistic, the score statistic, Peduzzi, Hardy, and Holford (1980)'s statistic, Lee and Koval's statistic (LK), and a sweep operator's statistic (SW). Five stopping criteria are used: {dollar}\chi\sp2{dollar} test based on a fixed {dollar}\alpha{dollar} level, minimum value of ERR, minimum value of the C{dollar}\sb{lcub}\rm p{rcub}{dollar} statistic (Hosmer, 1989), minimum value of the Akaike information criterion (Akaike, 1974), and minimum value of Schwarz's criterion (Schwarz, 1978).;Apparent error tate (ARR) tends to underestimate true error rate (ERR). In our study, estimated true error rate (ERR) is obtained by ERR = ARR + {dollar}\\omega{dollar}, where {dollar}\\omega{dollar} is from Efron (1986)'s parametric estimate of bias for ARR.;We use Monte Carlo simulation with both multivariate normal and multivariate binary independent variables; we implement the simulation with SAS/IML programs. We then analyze the experimental design to see which factors of the distribution of independent variables affect various outcomes.;As a result, we recommend the best {dollar}\alpha{dollar} level for the {dollar}\chi\sbsp{lcub}(\alpha){rcub}{lcub}2{rcub}{dollar} stopping criterion. Second, we compare the order of variables selected by different selection criteria. Third, we investigate the effects of different structures of predictor variables on ARR, {dollar}\\omega{dollar}, and ERR. Fourth, we compare the sizes of subset models determined by different stopping criteria. Finally, we compare the performances of selection and stopping criteria in terms of ERR.
Recommended Citation
Lee, Kang-in, "Topics In Forward Stepwise Logistic Regression" (1994). Digitized Theses. 2358.
https://ir.lib.uwo.ca/digitizedtheses/2358