When we run an EFA in SPSS we get factor scores with a mean of 0 and a SD of 1. When we run a CFA in MPlus and generate factor scores using the MLM estimation (because we have sample weights) our factor scores means are close to 0 but the SD come out to values such as 0.15767 or 0.16517. We expected to get SD of 1. Can you tell us why that is? Is there something we are doing wrong? Is it a problem if we use the factor scores generated from MPlus with the factor scores we generated from SPSS?
It is well known that estimated factor scores do not have the same distribution as the factor distribution in the estimated model, nor do they have the same relationships to other variables. For example, the variance of the estimated factor scores is typically smaller than the model-estimated factor variance.
Perhaps SPSS standardizes the estimated factor scores.
Jack Noone posted on Wednesday, November 25, 2009 - 1:45 pm
I am in exactly the same position. I want to examine the relationship between certain variables and some factor scores in a hierarchical regression. Unfortunately the regression coefficients using the Mplus fscores (from a CFA) are completely different to those using SPSS factor scores (PAF). But the spss Fscores correlate very highly with the mplus factor scores (.95).
The intercorrelations between the mplus fscores are MUCH higher than the SPSS factor scores (.75 v .4 respectively) and this is mucking up the regressions I think.
Can you offer a solution or direct me towards another source of info? It doesn't seem right to use SPSS generated factor scores when the prior anlaysis was done in mplus.
Perhaps your SPSS factors are obtained via EFA using orthogonal rotation. I assume the CFA uses correlated factors. Also, compared to an EFA with oblique rotation, a CFA can induce too high factor correlations due to fixing all cross-loadings at zero so that too much of the item correlations go via the factors. See the 2009 Asparouhov-Muthen article in the SEM journal on ESEM. You can get factor scores from ESEM EFA and not have to take the CFA step. See ESEM examples in the Version 5.1 Examples Addendum on our web site.
Jack Noone posted on Wednesday, November 25, 2009 - 4:30 pm
Thank you for your help. it was a promax rotation which assumes correlated factors. I'll check out the examples
Jack Noone posted on Thursday, November 26, 2009 - 12:47 pm
Hello Bengt. Above you said
It is well known that estimated factor scores do not have the same distribution as the factor distribution in the estimated model, nor do they have the same relationships to other variables.
Tucker, L.R. (1971). Relations of factor score estimates to their use. Psychometrika, 36, 427-436.
Perhaps an easier one to read is
Skrondal, A. and Laake, P. (2001). Regression among factor scores. Psychometrika 66, 563-575.
The topic should also be in factor analysis books, at least in the classic one by Lawley.
Jack Noone posted on Thursday, November 26, 2009 - 7:01 pm
Thank you Bengt, I really appreciate this
Elina Dale posted on Sunday, April 21, 2013 - 5:40 pm
Dear Dr. Muthen,
I have 3 questions re: factor scores obtained in MPlus using Bayes estimator in a two-level CFA model.
1. On slide 120 in your lecture MPlus Short Courses, Topic 1 (2009), it says that one of the uses of factor scores is as proxies for latent variables, which I understand. But then you make a point that "Independent variables in a model - not as dependent". Why? I would like to use factor scores in estimating the effect of treatment (financial incentives) on motivation (factor scores based on CFA). Would this be an incorrect approach? I know SEM would be ideal but as the first step, I need to use factor scores as proxies.
2. Is it correct that you use the Regression method (as opposed to Bartlett's for ex) in estimating factor scores? Are the obtained factor scores using Bayes estimator in MPlus closer to the "true" score than if I simply used the sum of the items or their mean?
3. How do I obtain factor determinacy? I have skewed categorical data and from the Guide (p.731) it seems FDeterminacy is only for continuous indicators. What to do with categorical? How can I see if estimated and true factor scores are correlated?
See the new FAQ Factor scores on the website. You should find all of your answers there.
Elina Dale posted on Monday, April 22, 2013 - 7:49 pm
Dear Dr. Muthen,thank you for the reference. It was very helpful. But I am failing to understand how factor scores relate to actual scores on each item making up the sub-scale. So, I'd like to make sure then that I've specified my model correctly. After getting my fscores, I sorted by fscore and looked at 5 top and 5 bottom ones. Then I looked at the responses on the actual items that were included in the factor. I don't understand why person J with 1,1,3,3 (for respective 4 items) has a >> fscore than person K with 4,4,1,3. All items are going in one direction, so a higher number means more/better. I thought it depended on which of the items had a higher loading, ie. items w/ higher loading weighted more in fscore. This would lead to K scoring 1 on the highest loading item but 4-3 on all other items, still getting a lower fscore than J who scored 3 on the highest loading item and 1 on the others. But this doesn't explain it as K scored 4, 4 on two highest loading items, while J scored 3, 3 on two highest loading items & 1's on two others. Still J has higher score than K. This doesn't make sense. This is the relevant part of the Input: Analysis: TYPE = twolevel; ESTIMATOR = BAYES; FBITERATIONS = 30000; PROCESSORS = 2; CHAINS = 2; Model:... Savedata: FILE IS fs.dat; SAVE=FSCORES (100);