Development of Influential Matrix for Detection of Outliers in Presence of Masking in Linear Regression using Survey Dat
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Authors
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Raju Kumar
ICAR-Indian Agricultural Statistics Research Institute, New Delhi
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Ankur Biswas
ICAR-Indian Agricultural Statistics Research Institute, New Delhi
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Deepak Singh
ICAR-Indian Agricultural Statistics Research Institute, New Delhi
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Tauqueer Ahmad
ICAR-Indian Agricultural Statistics Research Institute, New Delhi
Keywords:
Eigenvectors; Extended Conditional Cook-statistic; Influence matrix; Outlier; Masking; Complex survey data; Linear regressionAbstract
Identification of outliers and influential points is crucial in linear regression, particularly when dealing with survey data. Earlier works by Li and
Valliant (2011, 2015) proposed diagnostic measures for detecting single influential observations in both unclustered and clustered survey data.
However, these methods face challenges when multiple influential subsets exist, primarily due to the phenomenon of masking, where the presence
of multiple outliers conceals their influence. In contrast, substantial advancements for non-survey data have been made, notably by Peña and Yohai
(1995) and Lawrance (1995), who introduced diagnostic procedures capable of detecting influential subsets under masking conditions. Peña and
Yohai (1995) developed an influence matrix defined as the matrix of uncentered covariances representing the effect of deleting each observation
on the entire dataset, with normalization to include univariate Cook’s statistics on the diagonal. Candidate outliers are identified by examining the
eigenvectors associated with the non-null eigenvalues of this matrix. Building on this concept, we have developed an influence matrix tailored for
survey data, enabling the detection of influential subsets even in the presence of masking. The proposed diagnostic is demonstrated using a real-life
survey dataset, highlighting how masked outliers can significantly affect both ordinary and survey-weighted least squares estimation.
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