On closeness between factor analysis and principal component analysis under high-dimensional conditions
Book Chapter
Liang, L, Hayashi, K, Yuan, KH. (2015). On closeness between factor analysis and principal component analysis under high-dimensional conditions
. 140 209-221. 10.1007/978-3-319-19977-1_15
Liang, L, Hayashi, K, Yuan, KH. (2015). On closeness between factor analysis and principal component analysis under high-dimensional conditions
. 140 209-221. 10.1007/978-3-319-19977-1_15
This article studies the relationship between loadings from factor analysis (FA) and principal component analysis (PCA) when the number of variables p is large. Using the average squared canonical correlation between two matrices as a measure of closeness, results indicate that the average squared canonical correlation between the sample loading matrix from FA and that from PCA approaches 1 as p increases, while the ratio of p/N does not need to approach zero. Thus, the two methods still yield similar results with high-dimensional data. The Fisher-z transformed average canonical correlation between the two loading matrices and the logarithm of p is almost perfectly linearly related.
