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.
Highlights
In dementia studies involving large community-based cohorts of elderly participants, screening tests are often administered to study participants in order to obtain a measure of cognitive function
We investigate the empirical performances of the proposed estimator in small to moderate samples
The items are described in details as below: 1. Do you remember my name?
Summary
In dementia studies involving large community-based cohorts of elderly participants, screening tests are often administered to study participants in order to obtain a measure of cognitive function. Item selection using multiple logistic regression often encounters serious estimation problems when applied to screening data in dementia. Bull et al (2002) extended Firth’s approach to multinomial logistic regression with nominal response categories, comparing it to maximum likelihood estimates and to maximum likelihood estimates corrected by an estimate of the asymptotic bias They showed that Firth’s penalized maximum likelihood estimator was superior to the other methods in small samples and Firth’s estimator was equivalent to the maximum likelihood estimator as sample size increased. We propose a double penalized maximum likelihood estimator for logistic regression models which combines Firth’s penalized likelihood approach with a second penalty term for ridge parameter which is capable of handling both separation and multicollinearity.
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