Li, Ying
(2014).
A twostep regression method with connections to partial least squares and the growth curve model.
Diss. (sammanfattning/summary)
Uppsala :
Sveriges lantbruksuniv.,
Acta Universitatis agriculturae Sueciae, 16526880
; 2014:87
ISBN 9789157681225
eISBN 9789157681232
[Doctoral thesis]

PDF
588kB 
Abstract
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 twostep regression method inspired by PLS (partial least squares regression) is proposed. The proposed new method is coupled to a novel application of the CayleyHamilton theorem and a twostep estimation procedure. In the twostep approach, the first step summarizes the information in the predictors via a bilinear model. The bilinear model has a Krylov structured withinindividuals design matrix, which is closely linked to PLS, and a betweenindividuals 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 twostep 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 twostep method is a nonalgorithmic approach. The bilinear model used in the first step gives a greater modelling flexibility than classical PLS. The proposed new twostep method has been extended to handle grouped data, especially data with different mean levels and with nested mean structures. Correspondingly, the new twostep 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 twostep method.
Authors/Creators:  Li, Ying  

Title:  A twostep regression method with connections to partial least squares and the growth curve model  
Series/Journal:  Acta Universitatis agriculturae Sueciae (16526880)  
Year of publishing :  2014  
Depositing date:  2014  
Volume:  2014:87  
Number of Pages:  58  
Papers/manuscripts: 
 
Place of Publication:  Uppsala  
Publisher:  Department of Energy and Technology, Swedish University of Agricultural Sciences  
ISBN for printed version:  9789157681225  
ISBN for electronic version:  9789157681232  
ISSN:  16526880  
Language:  English  
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 TwoStep Regression Method, Growth Curve Model, Krylov Space, MLE, PLS  
URN:NBN:  urn:nbn:se:slu:epsilone2209  
Permanent URL:  http://urn.kb.se/resolve?urn=urn:nbn:se:slu:epsilone2209  
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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