FSCORES - why has my variance changed? PreviousNext
Mplus Discussion > Confirmatory Factor Analysis >
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 Jon Heron posted on Wednesday, October 06, 2010 - 1:41 am
Hi Bengt/Linda,

I'm fitting a 3-factor model where one factor is constrained to be N(0,1) and the other two have means/vars freely estimated.

I've exported the FSCORES for some further analysis however the sample statistics for these estimated fscores show a cov matrix markedly different from the cov matrix of the latent variables in my model. In particularly the variances are much lower and the variance of my constrained factor is now around 0.7

I'm willing to accept that this all may be due to the estimation of something manifest from my underlying latent variable.


My issue comes with the second stage of my model. I have decided, quite late in the day, that a metric of N(100,15) might be more appealing to the reader than the original N(0,1) so would like to rescale my derived fscore variables. The thing is, do I base this rescaling on my initial constraint of N(0,1) or the observed data which is about N(0.1, 0.7). Clearly this could have quite an impact on parameter estimates.


many thanks, Jon
 Linda K. Muthen posted on Wednesday, October 06, 2010 - 9:58 am
Factor scores and factors are not equivalent and will not have the same means, variances, and covariances. See

Skrondal, A. and Laake, P. (2001). Regression among factor scores. Psychometrika 66, 563-575.

for further information.
 Jon Heron posted on Thursday, October 07, 2010 - 2:35 am
OK, thanks Linda

Jon
 Jon Heron posted on Wednesday, November 10, 2010 - 2:46 am
Hi Bengt/Linda,

carrying on from my question above I have begun to investigate Plausible Values as I was unhappy with my FSCORES.

I changed my estimator from WLSMV to BAYES,
commented out my scale-factor commands
and added the data-imputation section as shown in example 11.6

This led to the following error which I dont understand:-

*** FATAL ERROR
Internal Error Code: VARIANCE COVARIANCE MATRIX NOT SUPPORTED WITH ESTIMATOR=BAYES.
An internal error has occurred. Please contact us about the error,
providing both the input and data files if possible.

please can you help?


I should add that I am currently running v6.0 thanks to our finance department dragging their feet with regard to my license payment.


many thanks, Jon
 Linda K. Muthen posted on Wednesday, November 10, 2010 - 10:41 am
Not all types of covariance structures are allowed with Psi and Theta for the Bayes estimator. More are allowed in Version 6.1. It sounds like you are in a disallowed situation.
 Jon Heron posted on Thursday, November 11, 2010 - 1:28 am
Thanks Linda
fingers crossed for v6.1

Jon
 Jon Heron posted on Monday, December 06, 2010 - 3:37 am
Update:

I have upgraded Mplus to v6.1 and I can now get my program to run, however I have to

(a) remove the commands refering to scale factors, and
(b) remove my equality constraints for residual correlations.

I have the same scale collected three times and each measured by 12 items. I would ideally like to correlate the residuals for each item through time and constrain these correlations to be equal.

This is the error I get:

*** FATAL ERROR
VARIANCE COVARIANCE MATRIX IS NOT SUPPORTED WITH ESTIMATOR=BAYES.
WITHIN A VARIANCE COVARIANCE BLOCK TWO OR MORE PARAMETERS ARE EQUAL.
ONLY FULL VARIANCE COVARIANCE BLOCKS WITH UNEQUAL PARAMETERS ARE ALLOWED.

is this likely to change with further updates or is this just a fact due to the maths?


thanks, Jon
 Linda K. Muthen posted on Monday, December 06, 2010 - 9:37 am
Try adding to the ANALYSIS command

ALGORITHM = GIBBS (RW);

See the Version 6.1 Language Addendum on the website with the user's guide for further information.
 Jon Heron posted on Tuesday, December 07, 2010 - 1:10 am
Thanks, I'll try this

I'm attempting to replicate in a 2-stage model, the findings from an earlier published paper of mine. This paper used a 1-stage model and WLSMV.

So far the plausible values approach is much closer than FSCORES in terms of both the latent variable covariance matrix as well as the estimated effect of a covariate, however it's not a perfect replication.

Perhaps the Bayesian estimation will never accurately reproduce WLSMV estimates.
 Bengt O. Muthen posted on Tuesday, December 07, 2010 - 6:11 pm
If there is missing data on the outcomes, this will throw off the comparison because WLSMV doesn't do MAR-like estimation which Bayes does. Also, but less important, Bayes uses full information and WLSMV uses second-order information only.

See also section 4.2 of the paper on our web site under Papers, Bayesian Analysis:

Asparouhov, T. & Muthén, B. (2010). Plausible values for latent variables using Mplus. Technical Report.
 Jon Heron posted on Wednesday, December 08, 2010 - 1:04 am
thanks Bengt
 Lesa Hoffman posted on Friday, February 03, 2012 - 4:03 am
Hi folks,

I am attempting to generate plausible factor scores values from a three-factor CFA that has some invariance constraints on the loadings, intercepts, and residuals (the factors are based on are the same scale administered to each person under three different conditions). Using v. 6.12 I get the same error message as earlier in this thread:

*** FATAL ERROR
VARIANCE COVARIANCE MATRIX IS NOT SUPPORTED WITH ESTIMATOR=BAYES. WITHIN A VARIANCE COVARIANCE BLOCK TWO OR MORE PARAMETERS ARE EQUAL. ONLY FULL VARIANCE COVARIANCE BLOCKS WITH UNEQUAL PARAMETERS ARE ALLOWED.

I have tried ALGORITHM=GIBBS(RW) and each of the other options. Is there something else I can try, or is this a modeling issue instead?

Thanks in advance for your assistance!
 Linda K. Muthen posted on Friday, February 03, 2012 - 8:54 am
Please send your output and license number to support@statmodel.com.
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