SPSSX Discussion

How does SPSS compute a factor correlation matrix?

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Handel, Richard W.

How does SPSS compute a factor correlation matrix?

Hi All,

I am running a PAF analysis using an oblique rotation (Direct Oblimin) and extracting two factors. I am curious what variables are being correlated to produce correlation coefficients in the “Factor Correlation Matrix.” When I save factor scores using each of the three methods for calculating factor scores available in SPSS and correlate the factor scores, I cannot reproduce the bivariate correlation that prints under the “Factor Correlation Matrix” output.

Thanks,

Rick

Richard W. Handel, Ph.D.

Professor

Department of Psychiatry and Behavioral Sciences

Eastern Virginia Medical School

825 Fairfax Avenue, Hofheimer Hall

Norfolk, VA. 23507

Phone: 757-446-7992

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD

Art Kendall

Re: How does SPSS compute a factor correlation matrix?

click <help><algorithms>
scroll down to "FACTOR"

Of course, a lot depend on the purposes of your analysis so YMMV with the suggestions below.

However, I see that you at an institution where you may be doing something in the social and behavioral sciences.

If so, if you did orthogonal rotation that would be more conventional and maximize discriminate validity.

Also if your application is dealing with items designed to be used as parts of a summative scale, you should consider the conventional approach of using unit weights. If you decide to do that
you would simply separately sum the items that load cleanly on each factor (reflecting items if necessary to have the high end of the scale be compatible with the construct you interpret as what is being measured in common by the items).

Unit weighting has long been shown to be robust across studies and sub-populations.

Most varieties of factor scores represent common and unique variance, whereas you would most likely be interested in the common variance.

Art Kendall
Social Research Consultants

Handel, Richard W.

Re: How does SPSS compute a factor correlation matrix?

In reply to this post by Handel, Richard W.

Art, Thanks. I'm in digest mode and responding from the website, so I don't know if the original text is being quoted. I couldn't find anything through a google search, and I can't access the help menu at all for the time being (any attempt to use the help menu locks up my computer). That's the first place I wanted to look! I'm waiting for my IT department to resolve the issue as an uninstall and reinstall of SPSS didn't take care of it. I'll take a look at the algorithms section once this issue is resolved.

Thanks,

Rick

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Rick Oliver-3

Re: How does SPSS compute a factor correlation matrix?

You could try looking here:

http://www-01.ibm.com/support/knowledgecenter/SSLVMB_22.0.0/com.ibm.spss.statistics.algorithms/alg_factor.htm

Rick Oliver
Senior Information Developer
IBM Business Analytics (SPSS)
E-mail: [hidden email]

From: Rick Handel <[hidden email]>
To: [hidden email]
Date: 10/31/2014 01:48 PM
Subject: Re: How does SPSS compute a factor correlation matrix?
Sent by: "SPSSX(r) Discussion" <[hidden email]>

Art, Thanks. I'm in digest mode and responding from the website, so I don't know if the original text is being quoted. I couldn't find anything through a google search, and I can't access the help menu at all for the time being (any attempt to use the help menu locks up my computer). That's the first place I wanted to look! I'm waiting for my IT department to resolve the issue as an uninstall and reinstall of SPSS didn't take care of it. I'll take a look at the algorithms section once this issue is resolved. Thanks, Rick ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD

Anthony Babinec

Re: How does SPSS compute a factor correlation matrix?

In reply to this post by Handel, Richard W.

The answer is: The factor correlation shown in the factor correlation matrix

is not numerically equivalent to deriving factor scores and then correlating

them. How to think about this is that the estimated factor scores have

an element of indeterminacy in them. One recent reference that goes into

this is Stanley Mulaik’s “Foundations of Factor Analysis, 2^nd edition.”

Tony Babinec

[hidden email]

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Handel, Richard W.
Sent: Friday, October 31, 2014 9:50 AM
To: [hidden email]
Subject: How does SPSS compute a factor correlation matrix?

Hi All,

Thanks,

Rick

Richard W. Handel, Ph.D.

Professor

Department of Psychiatry and Behavioral Sciences

Eastern Virginia Medical School

825 Fairfax Avenue, Hofheimer Hall

Norfolk, VA. 23507

Phone: 757-446-7992

Kirill Orlov

Re: How does SPSS compute a factor correlation matrix?

Rick, these are basic important things of factor analysis.
Let A be factor loading matrix before rotation, S be structure matrix and P be pattern matrix after oblique rotation.
(Geometrically all the three matrices are the coordinates of the same cloud points, the variables; the difference is that A are coordinates in orthogonal axes, S are perpendicular coordinates in nonorthogonal axes, and P are skew coordinates in those nonorthogonal axes.)

Then
A*Q=S
S*inv(Q)=A
A*inv(Q)'=P
P*Q'=A
where Q is the nonorthogonal rotation matrix.
Q'*Q=C is the matrix of correlations between the oblique factors (i.e. the axes in S and P).

Correlating the saved factor scores would not reproduce C exactly (or even close enough) because factor scores are inexact, they are only reasonable approximations. (You can never know factor scores exactly, and this is one thing which distinguishes factor analysis from principal component analysis.)

Hi All,

I am running a PAF analysis using an oblique rotation (Direct Oblimin) and extracting two factors. I am curious what variables are being correlated to produce correlation coefficients in the “Factor Correlation Matrix.” When I save factor scores using each of the three methods for calculating factor scores available in SPSS and correlate the factor scores, I cannot reproduce the bivariate correlation that prints under the “Factor Correlation Matrix” output.

Thanks,

Rick

Richard W. Handel, Ph.D.

Professor

Department of Psychiatry and Behavioral Sciences

Eastern Virginia Medical School

825 Fairfax Avenue, Hofheimer Hall

Norfolk, VA. 23507

Phone: 757-446-7992

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD

Handel, Richard W.

Re: How does SPSS compute a factor correlation matrix?

In reply to this post by Handel, Richard W.

>Date: Fri, 31 Oct 2014 18:04:08 -0500
>From: Anthony Babinec <[hidden email]>
>Subject: Re: How does SPSS compute a factor correlation matrix?

>The answer is: The factor correlation shown in the factor correlation matrix

>is not numerically equivalent to deriving factor scores and then correlating

>them. How to think about this is that the estimated factor scores have

>an element of indeterminacy in them. One recent reference that goes into

>this is Stanley Mulaik's "Foundations of Factor Analysis, 2nd edition."

>Tony Babinec

Thanks, Tony!!!

Rick

=====================
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