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<p>This paper presents a method for outlier detection in linear mixed models (LMMs) in the presence of collinearity among explanatory variables. To address the parameter instability induced by collinearity, the proposed approach incorporates random linear constraints as a regularization technique. The detection process is based on the variance shift outlier model, which formalizes an outlier as an observation with an inflated error variance. We derive parameter estimates for the constrained LMM and develop both score and likelihood ratio tests to statistically assess the variance shift for individual observations. A simulation study evaluates the power of these proposed tests under various conditions. Because the null distributions of the test statistics are non-standard, critical values are obtained using a parametric bootstrap procedure. Finally, the practical utility of the methodology is demonstrated through applications to real-world datasets.</p>

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Identifying Outliers Using the Variance Shift Method in the Linear Mixed Model Under Linear Stochastic Constraint

  • 期刊论文

  • 发表日期：

    2026年2月17日

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  • Kazem Gharbaghi,
  • Babak Babadi,
  • Abdolrahman Rasekh

摘要

This paper presents a method for outlier detection in linear mixed models (LMMs) in the presence of collinearity among explanatory variables. To address the parameter instability induced by collinearity, the proposed approach incorporates random linear constraints as a regularization technique. The detection process is based on the variance shift outlier model, which formalizes an outlier as an observation with an inflated error variance. We derive parameter estimates for the constrained LMM and develop both score and likelihood ratio tests to statistically assess the variance shift for individual observations. A simulation study evaluates the power of these proposed tests under various conditions. Because the null distributions of the test statistics are non-standard, critical values are obtained using a parametric bootstrap procedure. Finally, the practical utility of the methodology is demonstrated through applications to real-world datasets.