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Explicit estimators of parameters in the Growth Curve model with linearly structured covariance matrices

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  • Ohlson, Martin
  • von Rosen, Dietrich

Abstract

Estimation of parameters in the classical Growth Curve model, when the covariance matrix has some specific linear structure, is considered. In our examples maximum likelihood estimators cannot be obtained explicitly and must rely on optimization algorithms. Therefore explicit estimators are obtained as alternatives to the maximum likelihood estimators. From a discussion about residuals, a simple non-iterative estimation procedure is suggested which gives explicit and consistent estimators of both the mean and the linear structured covariance matrix.

Suggested Citation

  • Ohlson, Martin & von Rosen, Dietrich, 2010. "Explicit estimators of parameters in the Growth Curve model with linearly structured covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1284-1295, May.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:5:p:1284-1295
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    References listed on IDEAS

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    1. Khatri, C. G., 1973. "Testing some covariance structures under a growth curve model," Journal of Multivariate Analysis, Elsevier, vol. 3(1), pages 102-116, March.
    2. 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.
    3. Sanjay Chaudhuri & Mathias Drton & Thomas S. Richardson, 2007. "Estimation of a covariance matrix with zeros," Biometrika, Biometrika Trust, vol. 94(1), pages 199-216.
    4. 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.
    5. Y. Fujikoshi & T. Kanda & N. Tanimura, 1990. "The growth curve model with an autoregressive covariance structure," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(3), pages 533-542, September.
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    Cited by:

    1. Veronika Kopčová & Ivan Žežula, 2020. "On intraclass structure estimation in the growth curve model," Statistical Papers, Springer, vol. 61(3), pages 1085-1106, June.
    2. Rastislav Rusnačko & Ivan Žežula, 2016. "Connection between uniform and serial correlation structure in the growth curve model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 149-164, February.
    3. Yuli Liang & Dietrich Rosen & Tatjana Rosen, 2021. "On properties of Toeplitz-type covariance matrices in models with nested random effects," Statistical Papers, Springer, vol. 62(6), pages 2509-2528, December.
    4. Hu, Jianhua & Liu, Fuxiang & Ahmed, S. Ejaz, 2012. "Estimation of parameters in the growth curve model via an outer product least squares approach for covariance," Journal of Multivariate Analysis, Elsevier, vol. 108(C), pages 53-66.

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