Journal of Data Science

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.

Abstract: Mixed effects models are often used for estimating fixed effects and variance components in continuous longitudinal outcomes. An EM based estimation approach for mixed effects models when the outcomes are truncated was proposed by Hughes (1999). We consider the situation when the longitudinal outcomes are also subject to non-ignorable missing in addition to truncation. A shared random effect parameter model is presented where the missing data mechanism depends on the random effects used to model the longitudinal outcomes. Data from the Indianapolis-Ibadan dementia project is used to illustrate the proposed approach