An evaluation of ridge estimator in linear mixed models: an example from kidney failure data

ABSTRACT

This paper is concerned with the ridge estimation of fixed and random effects in the context of Henderson's mixed model equations in the linear mixed model. For this purpose, a penalized likelihood method is proposed. A linear combination of ridge estimator for fixed and random effects is compared to a linear combination of best linear unbiased estimator for fixed and random effects under the mean-square error (MSE) matrix criterion. Additionally, for choosing the biasing parameter, a method of MSE under the ridge estimator is given. A real data analysis is provided to illustrate the theoretical results and a simulation study is conducted to characterize the performance of ridge and best linear unbiased estimators approach in the linear mixed model.

KEYWORDS:

• Ridge regression
• random effects
• linear mixed model
• variance modeling
• mean-square error

AMS SUBJECT CLASSIFICATION:

• 62J07
• 62J05

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Suppose that there exist estimates of the variance components within G and R. Then the resulting estimator obtained by replacing G and R by their estimates is the feasible estimator.

2 The abbreviations ‘Cov. Struc.’ and ‘Est. Met. for Cov. Par.’ refer to ‘Covariance Structures’ and ”Estimation Methods for Covariance Parameters”.

3 The abbreviation ‘Cov. Par.’ refers to ‘Covariance Parameters’.

4 There is not too much difference between the results of ML and REML covariance estimates, i.e. ${\hat{k}}_h^{\mathrm{ML}}=0.023888292$ and ${\hat{k}}_h^{\mathrm{REML}}=0.023887922$.