Electronic Journal of Statistics

Restricted likelihood ratio testing in linear mixed models with general error covariance structure

Andrea Wiencierz, Sonja Greven, and Helmut Küchenhoff

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Abstract

We consider the problem of testing for zero variance components in linear mixed models with correlated or heteroscedastic errors. In the case of independent and identically distributed errors, a valid test exists, which is based on the exact finite sample distribution of the restricted likelihood ratio test statistic under the null hypothesis. We propose to make use of a transformation to derive the (approximate) null distribution for the restricted likelihood ratio test statistic in the case of a general error covariance structure. The method can also be applied in the case of testing for a random effect in linear mixed models with several random effects by writing the model as one with a single random effect and a more complex covariance structure. The proposed test proves its value in simulations and is finally applied to an interesting question in the field of well-being economics.

Article information

Source
Electron. J. Statist., Volume 5 (2011), 1718-1734.

Dates
First available in Project Euclid: 13 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1323785606

Digital Object Identifier
doi:10.1214/11-EJS654

Mathematical Reviews number (MathSciNet)
MR2870148

Zentralblatt MATH identifier
1271.62096

Keywords
Linear mixed model penalized splines likelihood ratio test correlated errors generalized least squares SOEP data subjective well-being

Citation

Wiencierz, Andrea; Greven, Sonja; Küchenhoff, Helmut. Restricted likelihood ratio testing in linear mixed models with general error covariance structure. Electron. J. Statist. 5 (2011), 1718--1734. doi:10.1214/11-EJS654. https://projecteuclid.org/euclid.ejs/1323785606


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