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

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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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Title: Contributions to partial least squares regression and supervised principal component analysis modeling
Author: Jiang, Yizhou
Advisor(s): Bedrick, Edward
Committee Member(s): Guindani, Michele
Huerta, Gabriel
Kang, Huining
Department: University of New Mexico. Dept. of Mathematics and Statistics
Subject: Partial Least Squares
PLS
Supervised Principal Component Analysis
SPCA
regression
modeling
multivariate
multicollinearity
high dimension data
multiple responses
statistical
Chemometrics
latent structure
latent variable
cross validation
algorithm
spline
fractional polynomial
LC Subject(s): Latent structure analysis.
Regression analysis.
Least squares.
Degree Level: Doctoral
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.
Graduation Date: December 2009
URI: http://hdl.handle.net/1928/10299


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