Page 269 - Contributed Paper Session (CPS) - Volume 2

CPS1854 Shonosuke S. et al.

Robust estimation and joint selection in
linear mixed models
1
2
2
Shonosuke Sugasawa ; Francis Hui ; Alan Welsh
1 Center for Spatial Information Science, the University of Tokyo
2 Mathematical Science Institute, Australian National University

Abstract
Linear mixed models have been widely used for analyzing clustered or
longitudinal data. Conventional methods assume normality for both random
effects and error terms, which could be sensitive to outliers and may produce
biased and inefficient estimates of the model parameters as well as inaccurate
prediction of random effects or future values. Although several robust
methods have been developed, they still suffer from their unstable
performances when the contamination is heavy. In this work, we modify the
estimating equations for both regression coefficients and random effects by
introducing normalized density weights, and propose robust estimator of the
model parameters as well as random effects. We provide MM-algorithm to
compute the minimizer of the objective function. Moreover, we consider the
joint selection of regression coefficients and random effects by introducing
adaptive lasso and adaptive group lasso penalty, respectively, and propose an
efficient algorithm to compute the robust and sparse estimator. We
demonstrate the proposed methods together with existing methods through
simulations studies and applications to real datasets.

Keywords
clustered data; estimating equation; divergence; linear mixed models; robust
estimation

1. Introduction
For analyzing clustered or longitudinal data, linear mixed models that can
adequately account for variability among clusters or individuals are widely
used. Conventionally, normality is assume for distributions of both random
effects and error terms, which often leads to unstable performance when there
exists outliers. In this work, we propose a new robust approach to estimation
in linear mixed models by modifying likelihood (estimating) equations for
regression coefficients and random effects with use of density weights. We
demonstrate that the modification is the same as considering an objective
function based on two-divergence. We provide a MM-algorithm for
calculating robust estimates of model parameters as well as random effects.

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