The Principal Component Logistic Regression And Its Application In The Kangaroo Skull Fossil Classification Research

With the development of paleontology and statistics, the statistical study of animals fossil has been strengthened. This paper mainly analyzes three types of "kangaroo skulls fossil "measurement data (see Appendix) given by British W.poole CSIRO in the early19th century. The names of three kinds of kangaroo species are M.giganteus, M.f.fuliginosus and M.f.melanops, a total of148observations,and each observation contains18variables. The purpose of this article is to establish the appropriate discrimination function model,and uses the test set to forecast classification effect. Dataset contains a relatively large number of missing values,so it is necessary to fill the missing values in the data analysis.This paper first introduces the way to fill missing values, followed by the principal component analysis to reduce the dimension of high-dimensional variables, and finally using logistic regression discriminant analysis method to establish the discriminant function model, and test the discriminant effect.The whole research process, with the aid of EXCEL software, R and SAS software, in order to find the suitable method to deal with high-dimensional data and the corresponding discriminant analysis method. This article not only to classified research on binary response variables, but also to do disorderly logistic regression discriminant analysis on the three-valued response variables.This paper is structured as follows. The chapter1is the introduction part,and mainly introduces the research background, the process of establishing model, the research purpose and research significance. The chapter2firstly introduces the filling method of the missing value, followed by the causes of dimensionality reduction using principal component analysis and specific application of principal component analysis method,and finally explaining the details of the logistic regression discriminant analysis method and its application, in addition, in the end of this chapter, a brief introduction to the way of thinking of the jackknife and cross-validation.The chapter3is introduced by the former method combines statistical analysis of the specific examples, mainly in the SAS software to do matrix calculations, principal component analysis and logistic regression analysis, and interpreting the results of statistical analysis.The Chapter4is to summarize all the research work, and put forward the advantages and disadvantages of the method and the direction of further research.