An anomaly arising in the analysis of processes with more than one source of variability

H S Battey and Peter McCullagh

Biometrika, 2024, vol. 111, issue 2, 677-689

Abstract: SummaryIt is frequently observed in practice that the Wald statistic gives a poor assessment of the statistical significance of a variance component. This paper provides detailed analytic insight into the phenomenon by way of two simple models, which point to an atypical geometry as the source of the aberration. The latter can in principle be checked numerically to cover situations of arbitrary complexity, such as those arising from elaborate forms of blocking in an experimental context, or models for longitudinal or clustered data. The salient point, echoing Dickey (2020), is that a suitable likelihood-ratio test should always be used for the assessment of variance components.

Keywords: Components of variance; Likelihood ratio; Nuisance parameter; Residual maximum likelihood; Wald statistic (search for similar items in EconPapers)
Date: 2024
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