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A novel trace test for the mean parameters in a multivariate growth curve model

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  • Hamid, Jemila S.
  • Beyene, Joseph
  • von Rosen, Dietrich

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 [Sigma]. 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.

Suggested Citation

  • Hamid, Jemila S. & Beyene, Joseph & von Rosen, Dietrich, 2011. "A novel trace test for the mean parameters in a multivariate growth curve model," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 238-251, February.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:2:p:238-251
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    References listed on IDEAS

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    1. von Rosen, Dietrich, 1989. "Maximum likelihood estimators in multivariate linear normal models," Journal of Multivariate Analysis, Elsevier, vol. 31(2), pages 187-200, November.
    2. Jian-Xin Pan & Kai-Tai Fang, 1996. "Influential observation in the growth curve model with unstructured covariance matrix," Computational Statistics & Data Analysis, Elsevier, vol. 22(1), pages 71-87, June.
    3. Jian-Xin Pan & Kai-Tai Fang, 1995. "Multiple outlier detection in growth curve model with unstructured covariance matrix," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(1), pages 137-153, January.
    4. Lin, Shu-Hui & Lee, Jack C., 2003. "Exact tests in simple growth curve models and one-way ANOVA with equicorrelation error structure," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 351-368, February.
    5. Jemila Seid Hamid & Dietrich Von Rosen, 2006. "Residuals in the Extended Growth Curve Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 121-138, March.
    6. Dietrich Rosen, 1995. "Residuals in the growth curve model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(1), pages 129-136, January.
    7. von Rosen, Dietrich, 1990. "Moments for a multivariate linear model with an application to the growth curve model," Journal of Multivariate Analysis, Elsevier, vol. 35(2), pages 243-259, November.
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    Cited by:

    1. Sayantee Jana & Narayanaswamy Balakrishnan & Dietrich Rosen & Jemila Seid Hamid, 2017. "High dimensional extension of the growth curve model and its application in genetics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(2), pages 273-292, June.
    2. Sayantee Jana & Narayanaswamy Balakrishnan & Jemila S. Hamid, 2020. "Inference in the Growth Curve Model under Multivariate Skew Normal Distribution," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 34-69, May.
    3. Jana, Sayantee & Balakrishnan, Narayanaswamy & Hamid, Jemila S., 2018. "Estimation of the parameters of the extended growth curve model under multivariate skew normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 111-128.

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