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A two-step estimation method for grouped data with connections to the extended growth curve model and partial least squares regression

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  • Li, Ying
  • Udén, Peter
  • von Rosen, Dietrich

Abstract

In this article, the two-step method for prediction, which was proposed by Li et al. (2012), is extended for modelling grouped data, which besides having near-collinear explanatory variables, also having different mean structure, i.e. the mean structure of some part of the data is more complex than other parts. In the first step, inspired by partial least squares regression (PLS), the information for explanatory variables is summarized by a multilinear model with Krylov structured design matrices, which for different groups have different size. The multilinear model is similar to the classical growth curve model except that the design matrices are unknown and are functions of the dispersion matrix. Under such a multilinear model, natural estimators for mean and dispersion matrices are proposed. In the second step, the response is predicted through a conditional predictor where the estimators obtained in the first step are utilized.

Suggested Citation

  • Li, Ying & Udén, Peter & von Rosen, Dietrich, 2015. "A two-step estimation method for grouped data with connections to the extended growth curve model and partial least squares regression," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 347-359.
    • Handle: RePEc:eee:jmvana:v:139:y:2015:i:c:p:347-359
    DOI: 10.1016/j.jmva.2015.03.011
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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. R. D. Cook & I. S. Helland & Z. Su, 2013. "Envelopes and partial least squares regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 851-877, November.
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