Generation of Non-Normal data(multigr... PreviousNext
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 Israr Qureshi posted on Monday, June 11, 2007 - 5:34 am
I am trying to perform Monte-Carlo study for between group analysis. My design include change in sample size, change in number of loadings for each construct and cahgning the normality of data. I was trying to test effects of violation of normality assumtion by setting skewness and kurtosis to 3. Is it possible to do so using Mplus MonteCarlo facility?
 Linda K. Muthen posted on Monday, June 11, 2007 - 9:53 am
You can easily change the sameple size, the number of factor indicators, and the size of the factors indicators in Mplus Monte Carlo simulations. There is no direct way of specifying the skewness of the generated data. You would need to create non-normal variables by mixing two normals.
 Israr Qureshi posted on Wednesday, June 13, 2007 - 6:01 am
Thank you Linda for your quick response.

Following is my Mplus input file. What changes should I make to generate non-normal a1-a3... d1-d3? I wish to keep other other conditions same i.e. loadings, relationship between latent variables etc.

Thank you for your help...

NAMES = a1-a3 b1-b3 c1-c3 d1-d3;
NREPS = 500;
SEED = 29845;
SAVE = c:\mplus\BNUC3L5H*.txt;
A BY a1@.7 a2@.8 a3@.9;
B BY b1@.7 b2@.8 b3@.9;
C BY c1@.7 c2@.8 c3@.9;
D BY d1@.7 d2@.8 d3@.9;
C ON A@.05;
C ON B@.20;
D ON C@.60;
D ON A@.35;
 Linda K. Muthen posted on Wednesday, June 13, 2007 - 9:33 am
See the following paper where the generation of non-normal data is shown:

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. Mplus inputs and outputs used in this paper can be viewed and/or downloaded from the Examples page.

This paper can be downloaded from the website under Papers.
 Johannes Meier posted on Monday, September 17, 2007 - 8:39 am
Linda, Bengt and all others

Thanks for many helpful comments I found recently in the threads of your discussion board.

Unfortunately, I couldn’t find an answer to the following (perhaps rather simple) question: I suppose the sample size of a multigroup analysis is dependant from the group number. Does this mean, when analysing the sample size with a Monte Carlo study (as proposed by Muthén & Muthén 2002), the resulting number of cases needed (X), is the minimum number for each group? Say 2 groups, sample size needed 2*X?

Thanks in advance,
 Linda K. Muthen posted on Tuesday, September 18, 2007 - 4:26 am
In the paper, multiple group analysis is not considered. You would need to do a multiple group simulation study to determine the number of observations needed for each group.
 Johannes Meier posted on Tuesday, September 18, 2007 - 2:00 pm
Thanks for your quick answer.

Sure you’re right, each group has its specific factor loadings, residual variances of the factor indicators and factor correlation, which should be considered.

Would it be possible to do a separate Monte Carlo study for each group (e.g. country) and of course to gain the same valid results as with a simulation of the whole model. This approach might be easier to handle, because of the differing sample sizes across groups, which are likely to be expected. Am I wrong to do so (regarding the model fit of the multiple group analysis)?
 Linda K. Muthen posted on Wednesday, September 19, 2007 - 7:39 am
Looking at each group separately seems like a good way to start. This is the same as looking at the groups together with no equality constraints across groups.
 Katherine Schaumberg posted on Saturday, April 27, 2019 - 2:27 pm
I am also attempting to run a Monte Carlo simulation study while specifying the skewness and kurtosis of a variable. I realize that one way to do this is to combine two normal distributions, though I am unsure of how to set the parameters for these distributions in order to achieve the desired skewness. Do you have any recommendations as to how to set these parameters.

Thank you,
 Bengt O. Muthen posted on Sunday, April 28, 2019 - 1:00 pm
You can use our skew-t feature discussed here:

Asparouhov, T. & Muthén B. (2015). Structural equation models and mixture models with continuous non-normal skewed distributions. Structural Equation Modeling: A Multidisciplinary Journal, DOI:10.1080/10705511.2014.947375. (Download Mplus inputs and outputs).
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