A variance shift model for detection of outliers in the linear mixed model |
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Authors: | Freedom N Gumedze Sue J Welham Robin Thompson |
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Affiliation: | a Department of Statistical Sciences, University of Cape Town, Private Bag, Rondebosch 7701, South Africa b Biomathematics and Bioinformatics, Rothamsted Research, Harpenden AL5 2JQ, UK c The University of Adelaide, Adelaide, SA 5005, Australia d School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, UK |
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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. |
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Keywords: | Likelihood ratio test Linear mixed model Multiple testing Outlier detection REML" target="_blank">REML Score test Variance shift outlier model |
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