Principal component analysis and factor analysis and SPSS software in detail the similarities and differences
Abstract: The principal component analysis and factor analysis (R-type) is widely used, but some papers and some textbooks SPSS software (see text) error. This paper points out these errors and their causes, and points out the harm caused by errors, in principle gives the principal component analysis and R-type factor analysis of the detailed mathematical model of similarities and differences between the methods are given to avoid making mistakes, and the SPSS software and made recommendations about textbooks.
Keywords: Principal component analysis; factor analysis; SPSS software; error; avoid
Let = (X1, ..., XP for the standardized random vector (p ge; 2), R is the correlation coefficient matrix, = (F1, ..., Fm main component vector, = (Z1, ..., Zm for the factor vector, m le; p , for the convenience factor, factor estimates, factor score with the same mark.
First, the issues raised and conclusions
Principal component analysis and R-type factor analysis is a multivariate statistical analysis in two important ways, the same dimension reduction, wide range of applications, but by popular SPSS software very wide process of the two methods is called the command, the user prone to error, what is causing these mistakes? Principal component analysis and factor analysis in the end R-similarities and differences between it? What harm would it go wrong?
The SPSS software in the economy, medicine and management in areas such as widespread use, particularly necessary to solve these problems.
After a number of papers and textbooks, some of SPSS software (see enclosure) due diligence analysis, comparison, the study draws:
Error reason: Some users and the author of the main component analysis and R-type factor analysis theory, similarities and differences and not through the steps towards solving the current SPSS software and the book does not improve the study of these two methods (for university teachers a great error of Health).
Conclusion: The principal component analysis and R-type factor analysis has 10 main difference, resulting in the principal component analysis and factor analysis of the quantitative evaluation system for different values of mixing different alternative quantitative error evaluation must be conducted separately.
Errors harm: economic efficiency of enterprises, competitiveness will bring a comprehensive evaluation of error assessment, medical diagnosis will bring misdiagnosis, wrong decision will bring down and so on.
Second, some users and its causes errors
After due diligence analysis, the following error:
① using principal component analysis theory of principal component analysis are not available, such as principal components analysis described the concept of error. ② solve the wrong principal component F, as = (the unit matrix, the significance of Table 1). ③ I do not know the name based on principal component F, of the principal components F named wrong. ④ Xk be a loss of explanatory variables. ⑤ carried out on the wrong rotation. ⑥ regression wrongly seeking F. ⑦ the factor analysis (with no rotation) error to as principal component analysis.
① using factor analysis on the principle of factor analysis are not available, such as factor analysis of the idea described in the main component analysis of the idea. ② I do not know the name factor Zi based on the factor Zis name wrong, as with a factor score function to name the factor Zi. ③ Xk be a loss of explanatory variables. ④ the principal component or factor that is wrong (meaning see Table 1). ⑤ I do not know the correlation coefficient matrix eigenvalue and factor the difference between contributions to vi, such as integrated function of factor score in Z = Zi vi Fully incorrectly taken as the characteristic value. ① using SPSS software, SPSS software itself, because no principal component analysis module, some users will use some of the modules of factor analysis to make the results of principal components, there has been confusion in the quantitative process. ② the SPSS software, the contents of the textbooks at the confusion factor analysis principal component analysis and factor analysis, resulting in some users confuse the two methods are wrong.
Can be seen from the above cause of the error is: Some users on the principal component analysis and R-type factor analysis of principle (principle see [4]), similarities and differences with the problem-solving steps to master not through SPSS software and the book does not present Both methods of improving.
Third, the principal component analysis and R-type factor analysis model comparing the similarities and differences
Here are the principal component analysis and R-type factor analysis of the similarities and differences compared with the current view is the comparison on the content and process, more thorough, more accurate, is to recognize the depth.
In common: principal component analysis and R-type factor analysis is the approximation of the covariance matrix, are intended to explain the reduced dimension data set. As an indicator of the positive of the specific [3], the standardization of indicators (SPSS software automatically), to determine the correlation matrix through the correlation between variables, find the correlation matrix eigenvalues and eigenvectors, principal components, the factor between the lines sex has nothing to do with the cumulative contribution rate (%), the variable does not appear to determine the main components is missing, the number of factors m, before the previous principal components m m a comprehensive contribution to the X Factor on the same, is maximized, are named according to principal components, factors and variables of the correlation coefficient.
Differences: variance, to maximiz
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