Comparison of Partial Least Squares and Principal Components Methods by Simulation
DOI:
https://doi.org/10.33095/jeas.v22i87.725Keywords:
/ انحدار المربعات الصغرى الجزئية- انحدار المركبات الرئيسية -المتغيرات الكامنة - تقليص الابعاد - التعدد الخطي ., Partial Least Squares Regression (PLSR); Principal Components Regression (PCR); latent variables, Dimension Reduction, MulticollinearityAbstract
Abstract
The methods of the Principal Components and Partial Least Squares can be regard very important methods in the regression analysis, where they are used to convert a set of highly correlated variables to a set of new independent variables, known components and those components are be linear and orthogonal independent from each other , the methods are used to reduce dimensions in regression analysis
In this paper , we use Partial Least Squares method with Non -linear Iterative partial least squares NIPALS(PLS1) algorithm and the principal components method with Singular Value Decomposition(SVD )algorithm , the simulation experiments are conduct to compare between their methods assuming that the error is normally distributed , several combination are supposed in simulation for both sample size, number of observation, dimension, and we find that the partial least squares method is better than the Principal Components method in two case, number of observation is greater than the number of variables(n>p) and the number of variables is greater than the number of observation (p>n).
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