Summary
It is well known how to analyse correctly data arising from auniresponse fixed or mixed effects model under a split-plot design. Many results are available for both canonical dependence pattern (compound symmetry) and more general patterns. Conversely, for the multiresponse case, there are only few results concerning the repeated measurements context. Some references are here given for amultiresponse analysis under multivariate compound symmetry. The aim of this paper is to propose a simple methodology for MANOVA testing procedures if a more general dependence pattern,i.e., circular autoregressive multiresponse dependence pattern, is assumed. Conservative thresholds are suggested in order to perform a powerful test even if only vague information is available about parameters appearing in this dependence pattern.
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References
Box, G. E. P. (1954), Some theorems on quadratic form applied in the study of analysis of variance problems, II. Effect of inequality of variance and correlation between errors in the two-way classification.Ann. Math. Stat., 25, 484–498.
Cochran, W. G. andCox, G. M. (1957),Experimental Designs, 2nd edn. New York: Wiley.
Cole, J. W. L. andGrizzle, J. E. (1966), Application of multivariate analysis of variance to repeated measurement experiments.Biometrics, 22, 810–828.
Gotway, C. A. andCressie, N. A. C. (1990), A spatial analysis of variance applied to soil-water infiltration.Water Resources Res., 26, 2695–2703.
Greenhouse, S. W. andGeisser, S. (1959), On methods in the analysis of profile data.Psychometrika, 24, 95–112.
Guseo, R. (1997), Split-plot design: extension and robustness aspects.Statistica Applicata, 9, 61–79.
Khattree, R. andNaik, D. N. (1994), Optimal test for nested designs with circular stationary dependence.Journ. of Stat. Planning and Inference, 41, 231–240.
Mortarino, C. (1997), Split-plot multirisposta: analisi di un modello misto in presenza di struttura di covarianza canonica e circolare.Note di Ricerca 5/1997, Dipartimento di Scienze Statistiche, Università di Udine.
Tan, W. Y. andGupta, R. P. (1983), On approximating a linear combination of central Wishart matrices with positive coefficients.Comm. Stat. Theory Meth., 12, 2589–2600.
Thomas, D. R. (1983), Univariate repeated measures techniques applied to multivariate data.Psychometrika, 48, 451–464.
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Mortarino, C., Guseo, R. Circular dependence in a multiresponse mixed model under a split-plot design. J. Ital. Statist. Soc. 9, 127–137 (2000). https://doi.org/10.1007/BF03178962
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DOI: https://doi.org/10.1007/BF03178962