Sparse Estimation Strategies in Linear Mixed Effect Models for High-Dimensional Data Application

Eugene A Opoku; Syed Ejaz Ahmed; Farouk S Nathoo

doi:10.3390/e23101348

Sparse Estimation Strategies in Linear Mixed Effect Models for High-Dimensional Data Application

Entropy (Basel). 2021 Oct 15;23(10):1348. doi: 10.3390/e23101348.

Authors

Eugene A Opoku¹, Syed Ejaz Ahmed², Farouk S Nathoo¹

Affiliations

¹ Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8P 5C2, Canada.
² Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S 3A1, Canada.

Abstract

In a host of business applications, biomedical and epidemiological studies, the problem of multicollinearity among predictor variables is a frequent issue in longitudinal data analysis for linear mixed models (LMM). We consider an efficient estimation strategy for high-dimensional data application, where the dimensions of the parameters are larger than the number of observations. In this paper, we are interested in estimating the fixed effects parameters of the LMM when it is assumed that some prior information is available in the form of linear restrictions on the parameters. We propose the pretest and shrinkage estimation strategies using the ridge full model as the base estimator. We establish the asymptotic distributional bias and risks of the suggested estimators and investigate their relative performance with respect to the ridge full model estimator. Furthermore, we compare the numerical performance of the LASSO-type estimators with the pretest and shrinkage ridge estimators. The methodology is investigated using simulation studies and then demonstrated on an application exploring how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer's disease.

Keywords: LASSO estimation; asymptotic bias and risk; high-dimensional data; linear mixed model; multicollinearity; pretest and shrinkage estimation; ridge estimation.