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A two-step regression method with connections to partial least squares and the growth curve model

Li, Ying (2014). A two-step regression method with connections to partial least squares and the growth curve model. Diss. (sammanfattning/summary) Uppsala : Sveriges lantbruksuniv., Acta Universitatis Agriculturae Sueciae, 1652-6880 ; 2014:87
ISBN 978-91-576-8122-5
eISBN 978-91-576-8123-2
[Doctoral thesis]

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Prediction of a continuous response variable from background data is considered. The independent prediction variable data may have a collinear structure and comprise group effects. A new two-step regression method inspired by PLS (partial least squares regression) is proposed. The proposed new method is coupled to a novel application of the Cayley-Hamilton theorem and a two-step estimation procedure. In the two-step approach, the first step summarizes the information in the predictors via a bilinear model. The bilinear model has a Krylov structured within-individuals design matrix, which is closely linked to PLS, and a between-individuals design matrix, which allows the model to handle complex structures, e.g. group effects. The second step is the prediction step, where conditional expectation is used. The close relation between the two-step method and PLS gives new insight into PLS; i.e. PLS can be considered as an algorithm for generating a Krylov structured sequence to approximate the inverse of the covariance matrix of the predictors. Compared with classical PLS, the new two-step method is a non-algorithmic approach. The bilinear model used in the first step gives a greater modelling flexibility than classical PLS. The proposed new two-step method has been extended to handle grouped data, especially data with different mean levels and with nested mean structures. Correspondingly, the new two-step method uses bilinear models with a structure similar to that of the classical growth curve model and the extended growth curve model, but with design matrices which are unknown. Given that the covariance between the predictors and the response is known, the explicit maximum likelihood estimators (MLEs) for the dispersion and mean of the predictors have all been derived. Real silage spectra data have been used to justify and illustrate the two-step method.

Authors/Creators:Li, Ying
Title:A two-step regression method with connections to partial least squares and the growth curve model
Series Name/Journal:Acta Universitatis Agriculturae Sueciae
Year of publishing :2014
Depositing date:2014
Number of Pages:58
I.Ying Li, Dietrich von Rosen and Peter Udén (2014). Statistical prediction methods with misspecifed model assumptions: an empirical robustness study. Submitted.
II.Ying Li and Dietrich von Rosen (2012). Maximum likelihood estimators in a two step model for PLS. Communications in Statistics - Theory and Methods, 41, 2503-2511.
III.Ying Li, Peter Udén and Dietrich von Rosen (2013). A two-step PLS-inspired method for linear prediction with group effect. Sankhyā A, 75, 96-117.
IV.Ying Li, Peter Udén and Dietrich von Rosen (2014). A two-step method for group data with connections to the extended growth model and PLS. Submitted.
Place of Publication:Uppsala
Publisher:Department of Energy and Technology, Swedish University of Agricultural Sciences
ISBN for printed version:978-91-576-8122-5
ISBN for electronic version:978-91-576-8123-2
Publication Type:Doctoral thesis
Full Text Status:Public
Agris subject categories.:U Auxiliary disciplines > U10 Mathematical and statistical methods
Subjects:(A) Swedish standard research categories 2011 > 1 Natural sciences > 101 Mathematics > 10199 Other Mathematics
Agrovoc terms:linear models, statistical methods, forecasting, data analysis, regression analysis
Keywords:A Two-Step Regression Method, Growth Curve Model, Krylov Space, MLE, PLS
Permanent URL:
ID Code:11638
Faculty:NJ - Fakulteten för naturresurser och jordbruksvetenskap
Department:(NL, NJ) > Dept. of Energy and Technology
Deposited By: Ying Li
Deposited On:11 Nov 2014 12:47
Metadata Last Modified:02 Dec 2014 11:09

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