Question

Score Factor Analysis

Asked by: tfewster500

I've performed a Factor Analysis on some data and I need to know how to score the solution on the data.  I realize that I can have SPSS create variables in my database that contain the factor scores automatically, what I need to do is be able to apply the scores to other sources of data.

My understanding is that there is some kind of scoring matrix as well as a rotation matrix that can be used to create the factor scores

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Asked On
2009-01-13 at 10:56:58ID24048652
Tags

SPSS

Topic

SPSS

Participating Experts
1
Points
500
Comments
7

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Answers

 

by: richdiesalPosted on 2009-01-13 at 11:28:37ID: 23366245

Your question is a little vague...  a factor analysis will produce different output depending on what kind of factor analysis it is - principle components, maximum likelihood, etc.  

Can you clarify "score the solution"?  Are you trying to produce a fit index?  Or are you just trying to look at unrotated/rotated factor loadings and trying to produce a solution?

 

by: tfewster500Posted on 2009-01-13 at 18:39:09ID: 23369595

The factor analysis that I've created is a rotated PCA.

When you run the factor analysis you have the option to save the factor scores.  SPSS will create new variables at the end of the data set (one for each factor) that contain each factor score.  What I'm trying to do is to be able to create these scores manually.

My assumption was that I could have SPSS export the "Factor Score Coefficient Matrix".  From this matrix, I could get the coefficient for each variable in the factor solution and then create the equations to calculate each factor score.  My reasons for doing this is that I need to create these factor scores on another data set using SQL.

When I follow this process (using the factor score coefficient matrix) I cannot match the scores that are created automatically by SPSS.  Not sure what I'm missing, although I wonder if the rotation has something to do with it?

 

by: richdiesalPosted on 2009-01-13 at 20:41:36ID: 23370044

You have the process right - the rotation shouldn't matter - I'm betting your missing the standardization step.  Assuming you're using the "regression" technique to compute factor scores, the whole process to do factor score computation by hand is:

1) Run factor analysis and produce the Component Score Coefficient Matrix
2) Standardize all values in the dataset (convert to z-scores)
3) Multiple each standardized score with its paired component score coefficient
4) Add all (z-score)*(coefficient) pairs within each case

That value should equal the one that SPSS produces - though you should be aware that very small rounding errors can produce drastically different results.  I would go at least 6 decimal places out on the values in the component score coefficient matrix, myself.

 

by: tfewster500Posted on 2009-01-14 at 07:12:15ID: 23373399

Thanks, I will look into that.

What I've done is standardize the variables myself in code and then use those standardized variables in creating the factor solution.  Would that have something to do with it?

 

by: richdiesalPosted on 2009-01-14 at 11:07:00ID: 23376216

That shouldn't matter either - if you are procedurally doing what I listed above, then there's not much left that it could be other than a coding error.

Throwing ideas out... you are standardizing the values within variables, right?  So that each z-score variable is individually centered on 0 (not across the entire dataset)?

 

by: tfewster500Posted on 2009-01-19 at 07:37:13ID: 23411476

Yes we are standardizing the variables individually so each has mean of 0 and standard deviation of 1.

We're at a point now were about 50% of our manual scores match the SPSS results exactly.  Really stuck on what this could be.

I'm going to grant you the points has you've steered us in the right direction.  If you have any other ideas that would be great.

 

by: richdiesalPosted on 2009-01-19 at 10:29:30ID: 23413189

Well, just from a troubleshooting point of view, is there anything consistently different between those scores that match and those that don't?  Perhaps the way the code is handling the standardization?  Rotation v. non-rotation?

20120131-EE-VQP-002

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