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Contributions to partial least squares regression and supervised principal component analysis modeling


Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/10299

Contributions to partial least squares regression and supervised principal component analysis modeling

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dc.contributor.author Jiang, Yizhou
dc.date.accessioned 2010-02-09T20:53:27Z
dc.date.available 2010-02-09T20:53:27Z
dc.date.issued 2010-02-09T20:53:27Z
dc.date.submitted December 2009
dc.identifier.uri http://hdl.handle.net/1928/10299
dc.description.abstract Latent structure techniques have recently found extensive use in regression analysis for high dimensional data. This thesis attempts to examine and expand two of such methods, Partial Least Squares (PLS) regression and Supervised Principal Component Analysis (SPCA). We propose several new algorithms, including a quadratic spline PLS, a cubic spline PLS, two fractional polynomial PLS algorithms and two multivariate SPCA algorithms. These new algorithms were compared to several popular PLS algorithms using real and simulated datasets. Cross validation was used to assess the goodness-of-fit and prediction accuracy of the various models. Strengths and weaknesses of each method were also discussed based on model stability, robustness and parsimony. The linear PLS and the multivariate SPCA methods were found to be the most robust among the methods considered, and usually produced models with good t and prediction. Nonlinear PLS methods are generally more powerful in fitting nonlinear data, but they had the tendency to over-fit, especially with small sample sizes. A forward stepwise predictor pre-screening procedure was proposed for multivariate SPCA and our examples demonstrated its effectiveness in picking a smaller number of predictors than the standard univariate testing procedure. en_US
dc.language.iso en_US en_US
dc.subject Partial Least Squares en_US
dc.subject PLS en_US
dc.subject Supervised Principal Component Analysis en_US
dc.subject SPCA en_US
dc.subject regression en_US
dc.subject modeling en_US
dc.subject multivariate en_US
dc.subject multicollinearity en_US
dc.subject high dimension data en_US
dc.subject multiple responses en_US
dc.subject statistical en_US
dc.subject Chemometrics en_US
dc.subject latent structure en_US
dc.subject latent variable en_US
dc.subject cross validation en_US
dc.subject algorithm en_US
dc.subject spline en_US
dc.subject fractional polynomial en_US
dc.subject.lcsh Latent structure analysis.
dc.subject.lcsh Regression analysis.
dc.subject.lcsh Least squares.
dc.title Contributions to partial least squares regression and supervised principal component analysis modeling en_US
dc.type Dissertation en_US
dc.description.degree Statistics en_US
dc.description.level Doctoral en_US
dc.description.department University of New Mexico. Dept. of Mathematics and Statistics en_US
dc.description.advisor Bedrick, Edward
dc.description.committee-member Guindani, Michele
dc.description.committee-member Huerta, Gabriel
dc.description.committee-member Kang, Huining

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