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Date:         Tue, 10 Mar 2009 14:57:24 -0500
Reply-To:     Anthony Babinec <tbabinec@sbcglobal.net>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Anthony Babinec <tbabinec@sbcglobal.net>
Subject:      Re: Reference for factor loading cut-off
In-Reply-To:  <1236700258.49b68c62a365c@webmail.sussex.ac.uk>
Content-Type: text/plain; charset="us-ascii"

It seems that the question of desirable loading size is tied up with the issue of the sample size on which the analysis is done. The source for the rules of thumb below is James Stevens' Multivariate Analysis textbook and citations therein. These rules would apply when the correlation matrix is being analyzed and PCA is the method of analysis:

Components with 4 or more loadings above .6 in absolute value are reliable regardless of sample size.

Components with about 10 or more loadings of .4 are reliable as long as N > 150.

Components with only a few low loadings should not be interpreted unless N > 300.

Here is another rule. Use the following formula:

n=302500/(500*Y+60*v-33)**2

where Y is the average distance between a sample and population loading, v is the hypothesized population loading, and n is the sample size required. For example, if an average loading is 0.5 and you wish to observe a discrepancy at least as small as .05 between your hypothesized loading and the sample-based one, you would need a sample size of at least 625. You can see in the above formula that smaller average loadings lead to larger required sample sizes, as does a smaller desired discrepancy.

Tony Babinec tbabinec@sbcglobal.net

"I believe the blues, the way things are today, is more important than it ever was." B.B. King

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