Model selection methods for multivariate linear partial least squares regression

Having large numbers of predictor variables or having more predictor variables than the number of observations is a serious problem in regression analysis. When a data set contains many predictor variables, multicollinearity can become an issue. Multicollinearity arises when predictor variables measure the same concept or when there is a linear relationship among them. These problems can cause high degrees of correlation and violate the assumption of Ordinary Least Square Analysis. As a result, it causes poor estimates of parameter estimation in regression analysis. A possible solution to this problem is a statistical method called `Partial Least Squares Regression?. PLSR allows for the study of regression in many situations that Multiple Linear Regression does not.In this thesis, PLSR has been studied in the analysis of obtaining the number of new predictor variables called `latent variables?. After obtaining the latent variables, this thesis is concerned with analyzing how many of these latent variables are the most relevant for describing the variability of predictor and response variables. Some model selection methods, such as two of the Multivariate Akaike Information Criterion which are studied by Bozdogan and Bedrick respectively, use PRESS values obtained from k-fold cross validation and Wold?s R criterion to obtain the optimum number of latent variables. The simulation study presented in this thesis has been performed to compare the performance of these criteria. The simulation results of MAIC, PRESS and Wold?s R were obtained from different number of observations and different numbers of predictor variables. These results show that for small-sized design matrices, all criteria achieved the true number of latent variables. However, the results for the other-sized design matrices varied greatly and they consistently showed different numbers of latent variables. The whole analysis, including all simulations and calculations, were done using MATLAB statistical program.