Comparison and Empirical Analysis between Principal Component Analysis and Factor Analysis

Abstract

We carry out an empirical analysis based on the study of the principal component analysis and the factor analysis, the data is in the 2012 China Statistical Yearbook [ 1 ] with 31 provinces and 9 major economic indicators. First by comparing three kinds of methods of factor analysis, we find out that the principal factor analysis method has the minimum sum of squared errors. Then we use the principal c omponent analysis and the principal factor analysis to extract two principal components and two principal factors from the economic indicators. Third, we calculate principal component scores, factor scores, and their comprehensive scores of the provinces under two methods. Finally, we find that the rankings of the provinces under the two methods are different, but the overall trends are consistent, and the trends are also consistent with the actual situations.