Date: Fri, 4 May 2001 12:08:15 -0400
Reply-To: "Edgar F. Johns" <efjmoj@MEDIAONE.NET>
Sender: "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From: "Edgar F. Johns" <efjmoj@MEDIAONE.NET>
Subject: Re: How to select variables in a factor analysis
In-Reply-To: <saf26ee1.001@GAOGWIA1.GAO.GOV>
In evaluating the variables in an Exploratory Factor Analysis (EFA), I
usually look at the Kaiser-Meyer-Olkin measure of sampling adequacy (MSA).
Rather than a cut-off value of .5, Kaiser developed the following rule of
thumb: <.5 = unacceptable; .5s = miserable; .6s = mediocre; .7s = middling,
.8s = meritorious; .9s = marvelous (Dziuban & Shirkey, 1974).Consequently,
if the overall value is less than .8, I'd consider it troubling. Dziuban &
Shirkey also provide a formula for obtaining the MSA for individual
variables.
I also look at the final communality estimate (when using an iterative
procedure for estimating communalities). If the final estimate is close to
zero, you've got problems with that variable (at least with the current data
and mix of other variables). What to do about it depends - you might drop
it, retain it but request fewer factors to rotate, use an extraction method
that doesn't use iteration to determine the communality estimates - on your
situation and intent.
Humphreys & Montanelli work produced the parallel analysis method for
determining the number of factors to retain. In using this method, you need
to calculate the eigenvalues from your correlation matrix with SMC's
(squared multiple correlations) in the diagonal (and no iterations) and
generate the scree from it.
Hope this helps.
Dziuban & Shirkey (1974). When is a correlation matrix appropriate for
factor analysis? Some decision rules. Psychological Bulletin, 81, 358-361.
Humphreys, & Montanelli. (1975). An investigation of the parallel analysis
criterion for determining the number of common factors. Multivariate
Behavioral Research, 19, 193-206.
Montanelli & Humphreys (1976). Latent roots of random data correlation
matrices with squared multiple correlations on the diagonal: A Monte Carlo
study. Psychometrika, 41, 341-348.
_____
Edgar F. Johns <EdgarJohns@obik.com>
Obik, LLC
2906 River Meadow Circle
Canton, MI 48188
Tel. 734.495.1292, Fax 734.495.1981
http://www.obik.com
-----Original Message-----
From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU]On Behalf Of
Arthur J Kendall
Sent: Friday, May 04, 2001 8:57 AM
To: SPSSX-L@LISTSERV.UGA.EDU
Subject: Re: How to select variables in a factor analysis
Sorry I don't have an exact citation.
Montanelli and Humphreys in the 70's factored many sets of random numbers.
They developed equations that input the number of cases, number of items,
and factor number and output a predicted eigenvalue. Users could
superimpose the curve from the predicted eigenvalues on the curve used in
the scree test. They suggested retaining only the number of factors where
the obtained eigenvalues were greater than those from the random data. I
went back over a couple dozen factor analyses where several stopping rules
were applied to ballpark the number of factors and interpretability
determined the number to retain. In most cases, the number retained
corresponded to (random eigenvalue + 1). This could be interpreted as 1
variable's more variance than would be obtained from random data.
If I were doing a FA today I would still use the approach of using a series
of stopping rules including M&H to ballbark the number to retain, but use
interpretability for the final determination.
>>> Chris Howden <chowden@DLWC.NSW.GOV.AU> 05/04/01 12:46AM >>>
<snip>
Speaking of communalities it seems to me that a good PhD thesis would be to
establish a test which evaluates if the amount of variance accounted for in
a factor analysis could be attributed to chance, or if it is significant.
Then only those variables that have a 'significant' amount of their variance
explained would be retained in the factor model. This would allow a variable
selection process similar to that used in multiple regression to be used in
factor analysis.
Christopher G Howden
Environmental Statistician
Dept Land & Water Conservation
(Office) 02 9895 7130
(Mobile) 0410 689 945
