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Two kinds of variance/covariance estimates in linear mixed models

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  • Zaixing Li

Abstract

For longitudinal data, the within-subject covariance matrix plays an important role in statistical inference and it is of great interest to investigate this. In the paper, two kinds of estimators are investigated for the random effect covariance matrix D 1 and the error variance σ 2 in linear mixed models. One is to estimate D 1 first and then to estimate σ 2 ; the other kind is to estimate σ 2 first and then for D 1 . Both kinds of estimators are consistent. The covariance matrices of these covariance estimators and the variances of these two error variance estimators are calculated. In particular, the mean square errors of these estimators are also derived for one dimensional random effects. Besides, a simulation study is conducted to investigate the performances of these estimators. Copyright Springer-Verlag 2013

Suggested Citation

  • Zaixing Li, 2013. "Two kinds of variance/covariance estimates in linear mixed models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 303-324, April.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:3:p:303-324
    DOI: 10.1007/s00184-012-0388-6
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    References listed on IDEAS

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    1. Zaixing Li & Lixing Zhu, 2010. "On Variance Components in Semiparametric Mixed Models for Longitudinal Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 442-457, September.
    2. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
    3. Cui, Hengjian & Ng, Kai W. & Zhu, Lixing, 2004. "Estimation in mixed effects model with errors in variables," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 53-73, October.
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