Monte Carlo ordinal CFA y* total vari...
Message/Author
 Doug Snee posted on Tuesday, June 16, 2009 - 3:46 am
Hello,

I just want to make sure that I haven't lost my mind. I'm doing some Monte Carlo analyses on CFAs with 2 correlated factors (4 items each), where each indicator is ordinal. One indicator for each factor cross-loads on the other factor. Each factor variance is fixed to 1.0.

For the population model, I use the following in the relevant part of the syntax:

MODEL population:

f1@1 f2@1;
f1 WITH f2@.3;
f1 BY u1-u4@.7 u5@.35;
f2 BY u5-u8@.7 u4@.35;
u1-u3@.51 u6-u8@.51 u4-u5@.2405;

(I specify thresholds next in the syntax because I'm simulating ordinal indicators with latent y*s. I also tell it to make them categorical earlier in the syntax.)

I just want to verify that this indeed should cause each y* variable to have a variance of 1.0 (in the population model).

For u1 for instance, .7^2 + .51 = 1.0.

For u4, .7^2 + .35^2 + 2*(.7*.3*.35) + .2405 = 1.0.

I am not crazy, right?
 Linda K. Muthen posted on Tuesday, June 16, 2009 - 8:17 am
This seems correct.
 Doug Snee posted on Tuesday, June 16, 2009 - 5:26 pm
Thank you, Linda! I was afraid I was losing it.

One related thing: If a particular estimated solution results in a variance >1 for a y*, as indicated by the above formulas, does this correspond to a situation in which Mplus flags the solution as inadmissable?

In other words, are the y* automatically scaled to have variance = 1 during estimation, meaning that a variance greater than 1 as indicated by the above formulas would indicate a negative error variance?

Doug
 Linda K. Muthen posted on Wednesday, June 17, 2009 - 9:20 am
A variance greater than one indicates a negative residual variance.
 Doug Snee posted on Wednesday, June 17, 2009 - 12:04 pm
Thank you, Linda.

One other thing that I realized is that somehow Mplus isn't producing the nonconvergence indicator variable. (On either p. 480 or 488 of the version 3 manual, at the bottom of the page, it mentions that a nonconvergence indicator variable is produced as part of the Monte Carlo output.) The variable somehow just doesn't appear in the results that are output from each MC run. (I'm using version 3).

Perhaps I need to enter some command to get it? Or it doesn't come out if you request the TECH9 output? (I did)
 Linda K. Muthen posted on Wednesday, June 17, 2009 - 2:16 pm
 Anton Dominicson  posted on Monday, January 23, 2017 - 6:57 pm
Hello,

If I may ask, my CFA models use marker items and have factor variances freed in order to compare factor means and variances across groups. How can I calculate residual variances from unstandardized loadings for their use in a montecarlo simulation? Or is there another way to study coverage and parameter and S.E. bias in the estimation of factor means and variances?

Thanks.
 Bengt O. Muthen posted on Tuesday, January 24, 2017 - 8:30 am
Not sure I understand the question. Residual variances are printed in the output of a real-data analysis. In Monte Carlo you have to decide how much unexplained variance you have in a factor indicator and that gives you the residual variance.