Log In
Home ISDSA Press Annual Meeting Certification

Trace:

isdsapress:books:isdsa2019:isdsa2019c9

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

isdsapress:books:isdsa2019:isdsa2019c9 [2020/05/04 01:53] (current)
ISDSA created
Line 1: Line 1:
 +**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

ISDSA About Membership Jobs at ISDSA Privacy ISDSA Press About Journal of ISDSA Books Annual Meeting Current Meeting Donate ISDSA is an exempt organization under section 501(c)(3) of the Internal Revenue Code. To make tax deductible contribution for the growth of ISDSA, click here.