Partial Least Squares Regression Model And Applications On Education Statistics

Partial Least Squares (PLS) is a new method of Multivariate Statistical Analysis, and it is an improvement of Ordinary Least Squares (OLS). In many problems, prediction equations are formed by the independent variables and the dependent variables, but collinearities among the independent variables will be found with the correlations of the independent variables, or with any number of independent variables, even far more than the number of observation. If we still use OLS to form the model, the parameter estimation and the steadies of the model will be poor. In many methods, PLS is a useful method for dealing with the collinearities.This paper discusses and researches the method of PLS, and mainly does following several aspects.First, the harm of the collinearity in the regression model is discussed, and several methods of dealing the collinearity are introduced. Second, the algorithm for univariate PLS and multivariate PLS is discussed, and the differences between univariate and multivariate PLS is clarified. Third, from the multivariate PLS, an opinion of extracting components is brought up, and it improves the algorithm of PLS with the thought of Principal Components Analysis and Canonical Correlation Analysis. The PLS method based on the thought of extracting components not only has the function of prediction, which is formed by original PLS method, but also can use the extracted components to do some work similarities to Principal Components Analysis and Canonical Correlation Analysis. For example, the extracted components can be used to explain the independent and dependent variables, just like the naming of the components of Principal Components Analysis and Canonical Correlation Analysis; and as Canonical Redundancy Analysis of Canonical Correlation Analysis, we can measure the variance in dependent and independent variables by canonical components; and the correlation between the system of independents and dependents can be judged by the correlation between the canonical components. A Matlab program is designed by the PLS algorithm based on the thought of extracting components, and the prediction equationsand all kinds of solutions will be obtained directly, when the original dates are input. Forth, the PLS method appeared in the field of chemicals, and now it has been used in the research of the economic problems. In this paper, the PLS method is used in the research of education. The college students, who major in some specialties, their scores of Entrance course and Specialized course are selected. Using this dates, the PLSR prediction equations are formed between the score of Entrance course and Specialized course. And in this example, the PLS method is compared with three other methods of forming prediction equations: Ordinary Least Squares, Principal Components Regression, and Backward variable selection. Results suggest that the PLSR prediction equations have the smallest influence, which is formed by the disturb errors based on the change of samples, so PLS is a useful method for forming prediction equations.