Principal Component Regression Outliers Diagnosis And Treatment,

With the development of the computer technology and the improvement of the experiment technology, there often are the regression problems which include more independent variables in medical data. Here, because of large numbers of variables, it can't avoid that there is asymptotic linear relationship among independent, namely multicollinearty. In order to settle this problem, we can use the principal component regression (PCR). However, outliers often appear in medical data. In this situation, outliers influence PCR model in the following ways: (1) Outliers effect variance-covariance matrix, consequently, they effect the construction of PCR model. Therefore, the classical principal component analysis (PCA) is very sensitive to anomalous observations. (2) The breakdown value of least squares regression is 0,so only one outlier can spoil the fitness of regression. Therefore, the LS regression part of PCR is sensitive to anomalous observations too. It is thus important to diagnostic the outliers before carrying out PCR method.This paper systemically discusses two PCR outlier diagnostic methods and one robust PCR method, namely the PCR two-step outlier diagnostic, a outlier diagnostic based on robust PCR including MVT and LMS methods, and a robust PCR introduced which combines ROBPCA (robust principal component analysis) and robust regression- LTS(Least trimmed squares) .I n this paper we have introduced The PCR two-step outlier diagnostic, a outlier diagnostic based on robust PCR including MVT and LMS methods'basic theories and corresponding diagnostic tools, then a foundation was proved to detect outliers depending on the value of diagnostic tools. About the robust PCR, we have also introduced it's basic theories and computing process of the establishment of robust model. Moreover, robust PCR produces a diagnostic plot to display and classify the outliers.All the medical data collected in the paper were analyzed on computer by the SAS 8.0 and MATLAB 7.1 software. Satisfactory conclusions and interpretations have been obtained. Moreover, we also compared these diagnostic methods, especially compare the robust principal component regression method with the classical principal component regression method and illustrate the advantage and shortcoming of each method .It is better to solve the outlier problem in PCR, and provide a theoretical basis for the popularized application of these methods in medical studies. With improvement of theory, algebra and relevant software, the outlier diagnostic methods and robust PCR should be more widely used.