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A variance shift model for detection of outliers in the linear mixed model

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  • Gumedze, Freedom N.
  • Welham, Sue J.
  • Gogel, Beverley J.
  • Thompson, Robin

Abstract

A variance shift outlier model (VSOM), previously used for detecting outliers in the linear model, is extended to the variance components model. This VSOM accommodates outliers as observations with inflated variance, with the status of the ith observation as an outlier indicated by the size of the associated shift in the variance. Likelihood ratio and score test statistics are assessed as objective measures for determining whether the ith observation has inflated variance and is therefore an outlier. It is shown that standard asymptotic distributions do not apply to these tests for a VSOM, and a modified distribution is proposed. A parametric bootstrap procedure is proposed to account for multiple testing. The VSOM framework is extended to account for outliers in random effects and is shown to have an advantage over case-deletion approaches. A simulation study is presented to verify the performance of the proposed tests. Challenges associated with computation and extensions of the VSOM to the general linear mixed model with correlated errors are discussed.

Suggested Citation

  • Gumedze, Freedom N. & Welham, Sue J. & Gogel, Beverley J. & Thompson, Robin, 2010. "A variance shift model for detection of outliers in the linear mixed model," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2128-2144, September.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:9:p:2128-2144
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    References listed on IDEAS

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    1. Rüdiger Lehmann & Michael Lösler & Frank Neitzel, 2020. "Mean Shift versus Variance Inflation Approach for Outlier Detection—A Comparative Study," Mathematics, MDPI, vol. 8(6), pages 1-21, June.
    2. Schützenmeister, André & Piepho, Hans-Peter, 2012. "Residual analysis of linear mixed models using a simulation approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1405-1416.
    3. Julio M. Singer & Francisco M.M. Rocha & Juvêncio S. Nobre, 2017. "Graphical Tools for Detecting Departures from Linear Mixed Model Assumptions and Some Remedial Measures," International Statistical Review, International Statistical Institute, vol. 85(2), pages 290-324, August.
    4. Emi Tanaka, 2020. "Simple outlier detection for a multi‐environmental field trial," Biometrics, The International Biometric Society, vol. 76(4), pages 1374-1382, December.
    5. Xiaowen Dai & Libin Jin & Anqi Shi & Lei Shi, 2016. "Outlier detection and accommodation in general spatial models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(3), pages 453-475, August.
    6. Pinho, Luis Gustavo B. & Nobre, Juvêncio S. & Singer, Julio M., 2015. "Cook’s distance for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 126-136.
    7. Ali Mohammed Baba & Habshah Midi & Nur Haizum Abd Rahman, 2022. "Spatial Outlier Accommodation Using a Spatial Variance Shift Outlier Model," Mathematics, MDPI, vol. 10(17), pages 1-19, September.

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