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isdsapress:books:isdsa2019:isdsa2019c9 [2020/05/04 01:53] (current)
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 +**On the Relationship between Factor Analysis
 +and Principal Component Analysis in
 +Kentaro Hayashi\\
 +University of Hawaii at Manoa, USA\\
 +Ke-Hai Yuan \\
 +University of Notre Dame, USA\\
 +**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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