Power Calculation with Categorical In...
Message/Author
 Jochen Mayerl posted on Wednesday, December 11, 2002 - 2:16 am
I want to determine power using a model with two continous latent variables measured by categorical indicators and two exogenous observed variables. The estimator is WLSMV.

My question: Is it possible to apply your method determing power using a Monte Carlo Study described in your paper “How to Use a Monte Carlo Study to Decide on Sample Size and Determine Power” (Structural Equation Modeling 2002, 9(4), 599-620) to my model described above?
If not, which procedure can be used to determine power using a model with categorical indicators (WLSMV)?
 Linda K. Muthen posted on Wednesday, December 11, 2002 - 10:40 am
Following is Bengt's answer to a similar question:

"Your model has dependent variables that are categorical and therefore the Satorra-Saris method which uses the non-central chi-square as you describe it is not applicable since it requires maximum-likelihood estimation while Mplus only offers weighted least squares estimation for such models. So, you have to do a Monte Carlo study using a population covariance matrix. Parts of this matrix can be obtained from your estimated model, under the RESIDUAL output. In this output you find the estimated covariance matrix for the residuals given predictors (say R) and the estimated slope matrix (say S). SAMPSTAT will produce the sample covariance matrix for your predictors (say C). The population matrix P
that you need is then obtained as:

P = S*C*S' + R

which can be computed by say SAS IML. Alternatively, you can obtain P using path analysis rules applied to your estimated model and using C, which might be simpler if you are not used to matrices.

In your Monte Carlo analysis using the population matrix P, you can misspecify your model as you suggested. The proportion of replications in which the chi-square test rejects the model at the 5% level is the estimate of the power to detect the misspecification. For example, in the table below, this value is .046."

CHI-SQUARE P-VALUES

Expected Observed
0.990 0.988
0.980 0.970
0.950 0.934
0.900 0.884
0.800 0.768
0.700 0.678
0.500 0.464
0.300 0.282
0.200 0.190
0.100 0.092
0.050 0.046
0.020 0.016
0.010 0.010
 Larry DeCarlo posted on Friday, June 13, 2003 - 10:46 am
I have a related question. In using Monte Carlo with categorical data and multiple groups, is it possible to specify DIFFERENT cutpoints across the two groups?
 Linda K. Muthen posted on Friday, June 13, 2003 - 11:00 am
In Version 2, it is not possible. In Version 3, it will be possible.
 Stephan posted on Monday, August 04, 2008 - 11:39 pm
Hello,
after reading the Muthén & Muthén paper on power estimation published in Structural Equation Modeling (2002) and also that on this website I'm wondering if there's an example with categorical indicator available. I've tried something out and got the following response: -Unknown class label: %C#1% - after I've added thresholds for categorical data to the example which is printed on p.14/15 in one of the paper mentioned above.
Could you recommend an example?
Thanks heaps.
Stephan
 Linda K. Muthen posted on Tuesday, August 05, 2008 - 6:14 am
Find an example in the user's guide similar to what you want to do. Then use the Monte Carlo counterpart of that example as a starting point. These examples come with Mplus and are also available on the website.

Note that we used TYPE=MIXTURE with one class in the paper even though we were not doing mixture modeling. This is because at that time Mplus only had Monte Carlo facilities for mixture. The Monte Carlo facilities have since been increased.