Abstract
We consider a parallel profile model which is useful in analyzing parallel growth curves of several groups. The likelihood ratio criterion for a hypothesis concerning the adequacy of a random-effects covariance structure is obtained under the parallel profile model. The likelihood ratio criterion for the hypothesis in the general one-way MANOVA model is also obtained. Asymptotic null distributions of the criteria are derived when the sample size is large. We give a numerical example of these asymptotic results.
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References
Anderson, T. W. (1984).An Introduction to Multivariate Statistical Analysis, 2nd ed., Wiley, New York.
Boik, R. J. (1988). The mixed model for multivariate repeated measures: validity conditions and an approximate test,Psychometrika,53, 469–486.
Chinchilli, V. M. and Elswick, R. K. (1985). A mixture of the MANOVA and GMANOVA models,Comm. Statist. Theory Methods,14(12), 3075–3089.
Geisser, S. and Greenhouse, S. W. (1958). An extension of Box's results on the use of theF distribution in multivariate analysis,Ann. Math. Statist.,29, 885–891.
Gleser, L. J. and Olkin, I. (1969). Testing for equality of means, equality of variances, and equality of covariances under restrictions upon the parameter space,Ann. Inst. Statist. Math.,21, 33–48.
Gleser, L. J. and Olkin, I. (1970). Linear models in multivariate analysis,Essays in Probability and Statistics (eds. R. C. Bose, I. M. Chakravarti, P. C. Mahalanobis, C. R. Rao and K. J. C. Smith), 267–292, Univ. of North Carolina Press, Chapel Hill.
Greenhouse, S. W. and Geisser, S. (1959). On methods in the analysis of profile data,Psychometrika,24, 95–112.
Huynh, H. and Feldt, L. S. (1970). Conditions under which mean square ratios in repeated measurements designs have exactF-distributions,J. Amer. Statist. Assoc.,65, 1582–1589.
Morrison, D. F. (1990).Multivariate Statistical Methods, 3rd ed., McGraw-Hill, New York.
Rao, C. R. (1965). The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves,Biometrika,52, 447–458.
Rao, C. R. (1975). Simultaneous estimation of parameters in different linear models and applications to biometric problems,Biometrics,31, 545–554.
Srivastava, M. S. (1987). Profile analysis of several groups,Comm. Statist. Theory Methods,16(3), 909–926.
Srivastava, M. S. and Carter, E. M. (1983).An Introduction to Applied Multivariate Statistics, North-Holland, New York.
Verbyla, A. P. and Venables, W. N. (1988). An extension of the growth curve model,Biometrika,75, 129–138.
Yokoyama, T. and Fujikoshi, Y. (1993). A parallel profile model with random-effects covariance structure,J. Japan Statist. Soc.,23, 83–89.
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Yokoyama, T. LR test for random-effects covariance structure in a parallel profile model. Ann Inst Stat Math 47, 309–320 (1995). https://doi.org/10.1007/BF00773465
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DOI: https://doi.org/10.1007/BF00773465