Sparse Estimation Strategies in Linear Mixed Effect Models for High-Dimensional Data Application
Date
2021
Authors
Opoku, Eugene A.
Ahmed, Syed Ejaz
Nathoo, Farouk S.
Journal Title
Journal ISSN
Volume Title
Publisher
entropy
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.
Description
Research is supported by the Visual and Automated Disease Analytics (VADA)
graduate training program.
Keywords
linear mixed model, ridge estimation, pretest and shrinkage estimation, multicollinearity, asymptomatic bias and risk, LASSO estimation, high-dimensional data
Citation
Opoku, E. A., Ahmed, S. E., & Nathoo, F. S. (2021). Sparse estimation strategies in linear mixed effect models for high-dimensional data application. entropy, 23(1348), 1-24. https://doi.org/10.3390/e23101348