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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
Swedish University of Agriculture Science, Sweden.
Swedish University of Agriculture Science, Sweden.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Swedish University of Agriculture Science, Sweden.
2015 (English)In: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 139, 347-359 p.Article in journal (Refereed) Published
Abstract [en]

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. (C) 2015 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
Elsevier , 2015. Vol. 139, 347-359 p.
Keyword [en]
Extended growth curve model; Grouped data; Krylov space; PLS; Two-step method
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-120037DOI: 10.1016/j.jmva.2015.03.011ISI: 000355891200022OAI: oai:DiVA.org:liu-120037DiVA: diva2:840023
Available from: 2015-07-06 Created: 2015-07-06 Last updated: 2015-07-06

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von Rosen, Dietrich
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Mathematical Statistics Faculty of Science & Engineering
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