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Biometrika 1992 79(1):1-11; doi:10.1093/biomet/79.1.1
© 1992 by Biometrika Trust
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Nonlinear component of variance models

P. J. SOLOMON1 and D. R. COX2

1Department of Statistics, University of Adelaide GPO Box 498, Adelaide SA 5001, Australia
2Nuffield College, Oxford OXl INF U.K.

General aspects of nonlinearity in the context of component of variance models are discussed, and two special topics are examined in detail. Firstly, simple procedures, both formal and informal, are proposed for describing departures from normal-theory linear models. Transformation models are shown to be a special case of a more general formulation, and data on blood pressure are analyzed in illustration. Secondly, an approximate likelihood is proposed and its accurate performance is examined numerically using examples of exponential regression and the analysis of several related 2x2 tables. In the latter example, the approximate score test has improved power over the Mantel-Haenszel test.

Key Words: Cumulant • Likelihood • Logit • Nonlinearity • Nonnormality • Score test • Transformation • Variance component


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