A Solution to Separation and Multicollinearity in Multiple Logistic Regression
Volume 6, Issue 4 (2008), pp. 515–531
Pub. online: 4 August 2022 Type: Research Article Open Access
4 August 2022
4 August 2022
Abstract: In dementia screening tests, item selection for shortening an existing screening test can be achieved using multiple logistic regression. However, maximum likelihood estimates for such logistic regression models often experience serious bias or even non-existence because of separation and multicollinearity problems resulting from a large number of highly cor related items. Firth (1993, Biometrika, 80(1),27-38) proposed a penalized likelihood estimator for generalized linear models and it was shown to re duce bias and the non-existence problems. The ridge regression has been used in logistic regression to stabilize the estimates in cases of multicollinear ity. However, neither solves the problems for each other. In this paper, we propose a double penalized maximum likelihood estimator combining Firth’s penalized likelihood equation with a ridge parameter. We present a simu lation study evaluating the empirical performance of the double penalized likelihood estimator in small to moderate sample sizes. We demonstrate the proposed approach using a current screening data from a community-based dementia study.