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 Daniel Rodriguez posted on Monday, March 31, 2003 - 8:00 am
Is there a way to assess power with LCGA?
 Linda K. Muthen posted on Monday, March 31, 2003 - 8:17 am
You can use the same strategy that is outlined in the following paper:

Muthén, L.K. and Muthén, B.O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 4, 599-620.
 Daniel Rodriguez posted on Monday, March 31, 2003 - 9:15 am
Hi, does this apply to the situation with ordered categorical indicator variables as well? Or do I just consider my indicators as non-normal factor indicators as in your example in the paper?
 Linda K. Muthen posted on Monday, March 31, 2003 - 3:45 pm
LCGA can have continuous or categorical indicators in Mplus. See Examples 25.11 and 25.11A for categorical indicators.
 Patrick Malone posted on Wednesday, May 28, 2003 - 7:26 am

I need to do a power analysis for an elaborate planned missingness design. It looks like I could do this using the techniques from the sample size and power 2002 paper, but for one thing: I'm interested in discriminant validity for a CFA, so the null hypothesis I need power for to reject is that the factor correlation equals one. It looks like the MONTECARLO output won't give me that. If I had a simpler design, I could use the power analysis approach from power.html, but I don't see how that would work with a mixture model (using classes to represent the planned missingness).

I could fall back and just use the estimated standard errors for the factor correlations from the MONTECARLO output, and not have it be formally "power." Any suggestions, though?

 bmuthen posted on Wednesday, May 28, 2003 - 8:32 am
Could you somehow turn the unit correlation into a test of a parameter being zero? I was first thinking of a second-order factor but didn't get far with that. What about loadings that are equal and rejecting that they are zero; can the problem be rephrased into that?
 Patrick Malone posted on Wednesday, May 28, 2003 - 11:33 am
I'm not sure how. Except for the missing data part, the problem is straightforward. Three correlated factors, with four items each -- I want to know if I can reject the hypothesis that the factor correlations (taken together or one at a time -- I'll take either one) are 1. The factors will be trivially correlated -- the indicators are measures of the same trait taken across three contexts.
 bmuthen posted on Thursday, May 29, 2003 - 6:07 pm
Sounds like you may have to do Monte Carlo simulation "externally", that is generating data, running Mplus using "RUNALL", and combining results from runs with unit and non-unit correlations. Lot of work.
 Patrick Malone posted on Friday, May 30, 2003 - 11:21 am
That did the trick; wasn't so bad.

Thanks for your help.
 Jason Bond posted on Thursday, October 07, 2004 - 5:12 pm
I have taken a look at several papers I have found on power analysis for LGM (Linda and Bengt's paper in SEM entitled "How to use a monte carlo study to decide on sample size and determine power", Bengt and Patrick Curran's paper in Psych methods entitled "General longitudinal modeling of individual differences in experimental designs: a latent variable framework for analysis and power estimation", as well as the power example on this web site - and if anyone knows of any more, I would most appreciate hearing of them) but I haven't found any that explicitly discuss how to get at power to detect the number of classes. And I'm not sure exactly how to even define the concept of power for detecting a given number of classes. Perhaps it could be stated as the power to detect an additional class, given that k have already identified, for various true membership proportions in that additional group (the effect size). That is just a thought. Anyway, any input on this topic would be greatly appreciated.

 Bengt O. Muthen posted on Tuesday, October 12, 2004 - 5:13 pm
You can define power as the probability of rejecting a k-1 class model when a k class model is correct or the probability of rejecting a k + 1 model when a k class model is correct. A paper is being prepared by Nylund et al on this topic which you can request from bmuthen@ucla.edu.
 mart eussen posted on Thursday, October 15, 2009 - 1:46 am
Dear Dr. Muthen,

We would like to perform Latent Class Analysis on 18 or 23 binary items within a sample of n=134. Possible covariates are sex and age. Would we have enough power for reliable analysis?

Thank you in advance for your time,

Mart Eussen
 Linda K. Muthen posted on Thursday, October 15, 2009 - 10:20 am
Whether you have enough power depends on the separation of classes. You would need more observations if classes are not well-separated and fewer observations if the classes are well-separated. You would need to do a Monte Carlo study to determine how many observations you would need. See on the website:

Muthén, L.K. & Muthén, B.O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 4, 599-620.
 luke fryer posted on Wednesday, September 08, 2010 - 8:33 am
Muthén and Muthén,

I have read your 2002 article and it was very helpful, conceptually. However, neither the paper nor the Manual seem to provide syntax examples for dichotomous data. I have a sample of 650, 30 dichotomous indicators and three factors. Fit is very good but as it is my first time analyzing non-continuous data, I want to be sure that my sample size is sufficient. Is syntax available for for such a model?

My results, if they are valid, will be very controversial. I want to get this right...


p.s. sorry for my flurry of posts...
 Linda K. Muthen posted on Wednesday, September 08, 2010 - 11:20 am
All of the examples in the user's guide have data that were generated using Mplus. The Monte Carlo inputs for these are available on the Mplus CD and also on the website. Find an example with dichotomous data and take a look at that.
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