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+**On the Relationship between Factor Analysis
+and Principal Component Analysis in
+High-Dimensions?
+**
+Kentaro Hayashi\\
+University of Hawaii at Manoa, USA\\
+hayashik@hawaii.edu
+Ke-Hai Yuan \\
+University of Notre Dame, USA\\
+kyuan@nd.edu
+**Abstract**. This article reviews the relationship between loadings from
+factor analysis (FA) and those from principal component analysis (PCA)
+when the number of variables p is large. While FA and PCA are substantively
+different methodologies, the two loading matrices are often
+close to each other. After defining how to measure the degree of closeness
+between the two loading matrices under rotational indeterminacy,
+the article reviews the conditions under which the two loading matrices
+agree with each other. Two well-known conditions for characterizing the
+two sets of loadings are given by Guttman (1956) and by Schneeweiss
+(1997), and they are further refined by Krijnen (2006). The relationship
+between these conditions is discussed, and results are provided showing
+that the two loading are closely related when p is large. Estimation
+methods are described to deal with conditions when sparsity does not
+hold in the covariance matrix and when p is not much greater than the
+sample size. Also, the problem of an increased bias in eigenvalues of the
+covariance matrix as p increases is also noted.
+**Keywords**: Bias in eigenvalues • Canonical correlation • Matrix norm.
+**DOI**: https://doi.org/10.35566/isdsa2019c9

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