Skew & Kurtosis test in growth mixtur... PreviousNext
Mplus Discussion > Latent Variable Mixture Modeling >
 Bieke De Fraine posted on Monday, February 07, 2005 - 5:54 am
I tested the fit of a two-class growth mixture model for a continuous outcome by looking at the tech13 output.
The two-sided multivariate skew test of fit gives a p-value of 0.150
The two-sided multivariate kurtosis test of fit gives a p-value of 0.120
I read that obtaining low p-values indicates that the model does not fit the data.

(1) Can I conclude this test does not reject the two-class model ?

(2) I found little information on the SK-test. Where can I find these two manuscripts:
* Muthén & Asparouhov (2002): Mixture testing using multivariate skewness and kurtosis
* Wang & Brown (2002): Residual diagnostics for growth mixture models: examining the impact of a preventive intervention.

(3) The SK testing should be preceded by outlier investigations. How do I perform such analyses ?
 Linda K. Muthen posted on Monday, February 07, 2005 - 9:02 am
1. Yes.
2. Muthen and Asparouhov is not yet available. I believe Wang and Brown will be coming out in JASA. You need to check with them about that.
3. There are many books that describe outlier detection and some programs do this automatically. Basically, it is just looking at univariate and bivariate distributions to identify extreme observations.
 Natalie posted on Thursday, June 09, 2011 - 12:30 pm
Can tech13 be used with a single-class model to obtain multivariate skew and kurtosis statistics for the variables included in the model? In other words, I'm not interested in using these statistics for model selection. I just want to test multivariate normality. If one can do this, can small p values be interpreted as signifying departure from multivariate normality?

Thank you,
 Linda K. Muthen posted on Thursday, June 09, 2011 - 2:04 pm
Yes and yes.
 WEN Congcong posted on Monday, August 22, 2016 - 8:24 am
Dear professors,

Longtime no see! I am now reading the paper of Bauer and Curran(2003): Distributional Assumptions of Growth Mixture Models: Implications for Overextraction of Latent Trajectory Classes.

They argue that finite mixture models not only identify latent classes, but also approximate intractable or complex distributions. They believe that nonnormality is required for the solution of the model to be nontrivial and is a sufficient condition for extracting multiple components. After reading their examples, I have some questions.

(1)Within the current framework of Mplus, can we test the normality or nonnormality of the aggregate model?

(2)In empirical studies, besides the information criterion and LRTs, should the nonnormality of the aggregate model be an essential condition or indicator of the necessity of multiple latent classes if the estimated number of classes is quite small?

(3)In monte carlo simulation studies, may we be able to specify the different aggregate kurtosis and skewness ? If it can be done, I think that we can approximate the extent of normality or nonnormality level under which a finite mixture model with known number of classes can have nontrivial and significant solutions.
 Bengt O. Muthen posted on Monday, August 22, 2016 - 1:46 pm
A mixture model implies that the outcomes are non-normal so I don't think you need to test for (non-)normality.

Instead, you can take the new approach of using non-normal within-class distributions as described in the paper on our website:

Muthén, B. & Asparouhov T. (2015). Growth mixture modeling with non-normal distributions. Statistics in Medicine, 34:6, 1041–1058. DOI: 10.1002/sim6388

Using this method indicates that the Bauer-Curran concerns were exaggerated.
 WEN Congcong posted on Monday, August 22, 2016 - 6:45 pm
Thanks a lot!
 WEN Congcong posted on Thursday, September 01, 2016 - 9:18 pm
Hello again, professor Muthen,

I plan to do a simulation study in the framework of factor mixture model. As Lubke and Neale mentioned,¡°When using factor mixture models, one should be aware of the fact that deviations from the assumed multivariate normality within class can lead to overextraction of classes.¡±

This point of view can be regarded as the corollary of the conclusions of Bauer and Curran.

Therefore, I have two questions.

(1)The aim of the multivariate normality is to guarantee the homogeneity of each latent class. The skew t distribution method can be applied to the mixture models and avoid overextraction of classes. In my opinion, for the within-class in FMM, the normality assumption can also be violated with the new method. Is it right?

(2)Is it now available for us to generate data with specified degrees of normality, such as skewness, kurtosis in Mplus?

I am looking forward to your recommendations for the simulation study and thank you in advance!

 Bengt O. Muthen posted on Friday, September 02, 2016 - 10:02 am
(1) Skew-t is applied to the within-class distribution so there is no longer a within-class normality assumption.

(2)Yes, you can specify population values for S and K, but note that samples have to very large for these values to be approximately attained.
 WEN Congcong posted on Friday, September 02, 2016 - 8:16 pm
Thank you very much! I will try my best to do this study.
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