Stepwise principal component regression

In this paper the PLS method was introduced as a new tool in calculating statistical receptor models. It was compared with the two most popular methods currently applied to aerosol data Chemical Mass Balance Model and Target Transformation Factor Analysis. The characteristics of the PLS solution were discussed and its advantages over the other methods were pointed out. PLS is especially useful, when both the predictor and response variables are measured with noise and there is high correlation in both blocks. It has been proved in several other chemical applications, that its performance is equal to or better than multiple, stepwise, principal component and ridge regression. Our goal was to create a basis for its environmental chemical application. 

Regression techniques that can deal with colinear data include stepwise regression, ridge regression, principal components regression, and partial least squares (PLS) regression. The last two approaches are discussed in Sections 4.2 and 4.3. 

In the NIRS technique, the spectra need to be processed by using either principal component regression (PCR), multiple linear regression (MLR), stepwise multiple linear regression (SMLR), maximum... 

None of the above approaches optimizes the relationship between NIR absorbances and analyte for a range of sample types. Derivative transformations have been found to be generally useful when stepwise multiple linear regression (SMLR) techniques are used. When multidimensional statistics are employed, e.g., partial least-squares (PLS), principal component regression (PCR), or neural nets, it has been observed in some cases that the untransformed log 1/R data can perform just as well in correlation coefficient and error terms as in any kind of transformation. It is considered that in some cases physical manifestations of the sample contained in the spectra provide valid and useful discriminant data. 

Leonard and Roy [ 194] recently reported QSAR 70-73 on the HIV protease inhibitory data of 1,2,5,6-tetra-o-benzyl-D-mannitols (62) studied by Bouzide et al. [195]. Several statistical techniques such as stepwise regression, multiple linear regression with factor analysis as the data preprocessing step (FA-MLR), principal component regression analysis (PCRA) and partial least square (PLS) analysis were appHed to identify the structural and physicochemical requirements for HIV protease inhibitory activity. 

Vector containing regressors Residual in X matrix after a factors Residual in y vector after a factors Root mean squares of error prediction Partial least-squares regression Principal component regression Stepwise multiple linear regression PLSR with only one y-variable... 

Principal component analysis (PCA) of the soil physico-chemical or the antibiotic resistance data set was performed with the SPSS software. Before PCA, the row MPN values were log-ratio transformed (ter Braak and Smilauer 1998) each MPN was logio -transformed, then, divided by sum of the 16 log-transformed values. Simple linear regression analysis between scores on PCs based on the antibiotic resistance profiles and the soil physico-chemical characteristics was also performed using the SPSS software. To find the PCs that significantly explain variation of SFI or SEF value, multiple regression analysis between SFI or SEF values and PC scores was also performed using the SPSS software. The stepwise method at the default criteria (p=0.05 for inclusion and 0.10 for removal) was chosen. 

To avoid over-fitting, a commonly used approach is to select a subset of descriptors to build models. GAs are widely used to select descriptors prior to using other statistical tools, such as MLR, to build models. Certainly, principal component analysis and PLS fitting are also widely used in reducing the dimensions of descriptors. Traditionally, stepwise linear regression is used to select certain descriptors to enter the regression equations. 

Nielsen, B.R., Stapelfeldt, H., Skibsted, L.H. 1997. Early prediction of the shelf-life of medium-heat whole milk powders using stepwise multiple regression and principal component analysis. Int. Dairy J. 7, 341-348. 

To establish a correlation between the concentrations of different kinds of nucleosides in a complex metabolic system and normal or abnormal states of human bodies, computer-aided pattern recognition methods are required (15, 16). Different kinds of pattern recognition methods based on multivariate data analysis such as principal component analysis (PCA) (8), partial least squares (16), stepwise discriminant analysis, and canonical discriminant analysis (10, 11) have been reported. Linear discriminant analysis (17, 18) and cluster analysis were also investigated (19,20). Artificial neural network (ANN) is a branch of chemometrics that resolves regression or classification problems. The applications of ANN in separation science and chemistry have been reported widely (21-23). For pattern recognition analysis in clinical study, ANN was also proven to be a promising method (8). 

Pratsinis, S. E., Zeldin, M. D., and Ellis, E. C. (1988) Source resolution of fine carbonaceous aerosol by principal component-stepwise regression analysis, Environ. Sci. Technol. 22, 212-216. 

Correlation ranking and stepwise regression procedures in principal components artificial neural networks modeling with application to predict toxic activity and human serum albumin binding affinity... 

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