Questions regarding factor analysis and principal component analysis, both here and elsewhere, reveal considerable confusion of terms, disagreements about requirements, different recommendations for different issues and so on. Different programs label the same output differently. There is a fairly bewildering number of choices of extraction, rotation and so on. In addition, there is confusion about exploratory vs. confirmatory factor analysis and how both differ from principal component analysis.

I studied factor analysis way back in the late 1990s. I've read a bunch of recent articles. I think I more or less know what I am doing. However, it would be good to know of some authoritative recent source; perhaps an edited collection.

Some quick searching on Amazon didn't reveal any obvious candidates; are there any?

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    $\begingroup$ Peter, my own opinion is that almost all issues of confusion you mention have been discussed and settled in good old thick books (such as Harman. Modern Factor Analysis). Linear classic PCA/FA seem to already stop developing. But most "disagreements" are yet about these classic versions. I suppose it is due to the vulgarization of their knowledge among students and even professionals, which is the reverse of the pop status of the techniques. The same as with linear regression: people and managers use it mechanically every day because it is "basic", and still, know it very superficially. $\endgroup$ – ttnphns Dec 22 '13 at 0:22
  • $\begingroup$ There has been work in journal articles e.g. by Joresgkog and others on ordinal data, by Muthen and others on missing data, etc. Maximum likelihood FA was barely possible when some of the old books were written (computer speed issue). But even on "old" stuff like sample size requirements, I've seen different advice in various places. $\endgroup$ – Peter Flom Dec 22 '13 at 0:33
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    $\begingroup$ If you think PCA is worth an entire book, you don't take FA very seriously, and vice versa. I doubt that the books focused on PCA (Jolliffe, Jackson) would be regarded as good treatments of FA by FA specialists or enthusiasts. I don't really know the reverse literature, but the reasons underlying confusion and controversy also imply that impartial, dispassionate treatments will be elusive. $\endgroup$ – Nick Cox Dec 22 '13 at 19:47

There was a conference in 2004 »Factor Analysis at 100. Historical Developments and Future Directions«.

An edited book of chapters based on conference presentations followed:

Cudeck/MacCallum. 2007. Factor Analysis at 100. Historical Developments and Future Directions. Lawrence Erlbaum.

From the preface:

This book is the result of a conference that was held at the University of North Carolina in the spring of 2004 to commemorate the 100 year anniversary of Spearman’s famous article. The purpose of the conference and of this book was to review the contributions of the last century that have produced the extensive body of knowledge associated with factor analysis and other latent variable models. The contributors also took the occasion to describe the main contemporary themes in statistical models for latent variables and to give an overview of how these ideas are being extended.

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By just looking at (or seeing) this

In 1977, [Yoshio Takane] earned his Ph. D. in Psychometrics from the Univeraity of North Carolina at Chapel Hill.

and this

Peter Flom received his Ph.D. in Psychometrics in 1999 from Fordham University, where he was a Presidential fellow.

it is possible to assume that you are looking for the book entitled "Constrained Principal Component Analysis and Related Techniques" authored solely by Yoshio Takane and published by CRC press in 2014

I think it is reasonably authoritative but please let us know if it is modern enough (Japanese version is dated 1995).

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    $\begingroup$ Neither a book nor especially recent, but Multivariate Behavioral Research published a dynamite issue about 10-12 years ago all about EFA and PCA. $\endgroup$ – rolando2 Dec 22 '13 at 17:38
  • $\begingroup$ @rolando2, could you track down the issue? $\endgroup$ – gung - Reinstate Monica Dec 22 '13 at 17:50
  • $\begingroup$ I did get my degree in psychometrics, but these days my work is almost all in statistics. 1995 is pretty old.... But maybe nothing major has been done recently. $\endgroup$ – Peter Flom Dec 22 '13 at 18:07
  • $\begingroup$ @rolando2, I follow with gung in my interest. $\endgroup$ – ttnphns Dec 22 '13 at 19:19
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    $\begingroup$ @gung and ttnphns: The journal issue I mentioned seems to have been in 1990, volume 25, judging from Wayne Velicer's publication list at uri.edu/research/cprc/Publications/Authors/WVelicer.htm. See #10, Velicer, W. F., & Jackson, D.N. (1990). Component analysis vs. common factor analysis: Some issues in selecting an appropriate procedure. Multivariate Behavioral Research, 25, 1-28. Also see the many references to articles from this issue in pareonline.net/pdf/v10n7.pdf. $\endgroup$ – rolando2 Dec 24 '13 at 2:57

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