Comparison Between Principal Components and Factor Analysis for Different Data
Ahmed Mohamed Mohamed Elsayed
Issue:
Volume 8, Issue 4, December 2022
Pages:
65-79
Received:
21 February 2022
Accepted:
21 March 2022
Published:
29 December 2022
DOI:
10.11648/j.ijsd.20220804.11
Downloads:
Views:
Abstract: Factor analysis (FA) is similar to the principal component analysis (PCA), but not the same. PCA can be considered as a basic of FA. PCA and FA aim to reduce dimension of a data, but the techniques are different. FA is clearly designed to identify the latent factors from the observed variables, PCA does not directly apply this aim. Eigenvalues of PCA are dispersed component loadings, with variance errors. FA assumes that the covariation of observed variables is due to the presence of latent variables. In contrast, PCA not depends on such causal relationship. If the factor model is incorrectly, then FA will give error results. PCA employs a transformation of the original data with no assumptions about the covariance matrix. PCA is used to determine linear combinations of the original variables and summarize the data set without losing information. For these reasons, we compared practically between FA and PCA using three different types of data. One of them is simulated data, and others are real data. R program is used for analysis the data, using suitable different packages and functions. Results are presented graphically and tabulated for the purposes of comparison. An obtained results interested for each data with three criteria: FA criterion is used to specify whereas a two factors are sufficient or not; the SS loadings specified the factor is worth keeping; the observed correlations between all original variables high or low; the Cattell's scree test, says to drop all further components after starting at the elbow. The PCA criterion, is used to determine the variable's importance, which have high Eigenvalue. The VRPC criterion is used to determine the variables tend to suitable factor.
Abstract: Factor analysis (FA) is similar to the principal component analysis (PCA), but not the same. PCA can be considered as a basic of FA. PCA and FA aim to reduce dimension of a data, but the techniques are different. FA is clearly designed to identify the latent factors from the observed variables, PCA does not directly apply this aim. Eigenvalues of P...
Show More
