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Difference PCA and Factor analysisMLAI/DimensionalityReduction 2020. 1. 23. 11:06
1. Overview
Both are dimension reduction techniques, but while Principal Component Analysis is used to reduce the number of variables by creating principal components, extracting the essence of the dataset in the means of artificially created variables, which best describe the variance of the data.
Factor Analysis tries to identify, unknown latent variables to explain the original data. Often principal axis factoring is used when there is interest in studying relations among the variables, while principal components are used when there is a greater emphasis on data reduction and less on interpretation.
2. Comparison
2.1 Communality
2.1.1 PCA
Unlike factor analysis, principal components analysis or PCA makes the assumption that there is no unique variance, the total variance is equal to the common variance. Recall that variance can be partitioned into a common and unique variance. If there is no unique variance then common variance takes up total variance (see figure below). Additionally, if the total variance is 1, then the common variance is equal to the communality.
2.1.2 Factor analysis
Factor analysis assumes that variance can be partitioned into two types of variance, common and unique. The total variance is made up of common variance and unique variance, and unique variance is composed of specific and error variance. If the total variance is 1, then the communality is $h^{2}$ and the unique variance is $1-h^{2}$.
3. Reference
https://stats.idre.ucla.edu/spss/seminars/efa-spss/
https://psych.wisc.edu/henriques/pca.html
https://www.displayr.com/factor-analysis-and-principal-component-analysis-a-simple-explanation/
https://community.jmp.com/t5/JMP-Blog/Principal-components-or-factor-analysis/ba-p/38347#
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