A novel trace test for the mean parameters in a multivariate growth curve model |
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Authors: | Jemila S. Hamid Joseph Beyene Dietrich von Rosen |
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Affiliation: | a Surveillance and Epidemiology, The Ontario Agency for Health Protection and Promotion, Canadab Division of Biostatistics, Dalla Lana School of Public Health, University of Toronto, Canadac Department of Clinical Epidemiology and Biostatistics, McMaster University, Canadad Department of Energy and Technology, Swedish University of Agricultural Sciences, Sweden |
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Abstract: | A trace test for the mean parameters of the growth curve model is proposed. It is constructed using the restricted maximum likelihood followed by an estimated likelihood ratio approach. The statistic reduces to the Lawley-Hotelling trace test for the Multivariate Analysis of Variance (MANOVA) models. Our test statistic is, therefore, a natural extension of the classical trace test to GMANOVA models. We show that the distribution of the test under the null hypothesis does not depend on the unknown covariance matrix Σ. We also show that the distributions under the null and alternative hypotheses can be represented as sums of weighted central and non-central chi-square random variables, respectively. Under the null hypothesis, the Satterthwaite approximation is used to get an approximate critical point. A novel Satterthwaite type approximation is proposed to obtain an approximate power. A simulation study is performed to evaluate the performance of our proposed test and numerical examples are provided as illustrations. |
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Keywords: | 62H10 62H15 62J10 62E15 62E17 |
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