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Biometrika 1991 78(4):779-785; doi:10.1093/biomet/78.4.779
© 1991 by Biometrika Trust
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Selection of covariables in the growth curve model

YASUNORI FUJIKOSHI1 and C. RADHAKRISHNA RAO2

1Department of Mathematics, Hiroshima University Hiroshima 730, Japan
2Department of Statistics, Penn State University University Park, Pennsylvania 16802, U.S.A.

The growth curve model introduced by Potthoff & Roy (1964) is a generalization of the multivariate analysis of variance model and is often employed to analyze longitudinal data, in which a single characteristic has been measured at p different occasions on each individual. Inferential problems of this model are studied by using analysis of covariance, i.e. partitioning the p measurements into the measurements of q response variables and p-q covariables. Rao (1965, 1966) and Grizzle & Allen (1969) discuss the possibility of using fewer than p-q covariables. In this paper we propose two types of formulation for the hypotheses of redundancy of a given set of covariables. The likelihood ratio criteria are obtained for testing the hypotheses. These results permit the use of information criteria such as aic for selection of the best subset of covariables.

Key Words: Growth curve model • Likelihood ratio test • Redundancy of covariables • Selection of covariables


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