Issues of skewness and kurtosis in GMMs PreviousNext
Mplus Discussion > Latent Variable Mixture Modeling >
 milan lee posted on Wednesday, May 28, 2014 - 8:22 am
Dear Dr.Muthen,
I am cleaning up my five-wave longitudinal data to try out Growth Mixture Modeling. Descriptive stat showed that the five repeated outcomes (y1-y5; all standardized scores) have moderate skewness (observed skewness is around 3.1) and high kurtosis (observed kurtosis is 8.0, on average). I believe that the skewness is partly driven by the existence of outliers (the highest Z score is 6.12). It seems like researchers typically delete them but I doubt it is a right way to do so in a context of GMMs. GMMs are supposed to capture non-normal data as suggested in many publications of yours. But since I could not find a paper that talked about outliers were handled before setting up GMMs, I am very confused at what exactly I should do at this point. Also, what should I do about the kurtosis issue in preparing for GMMs?

Thank you very, very much!
 milan lee posted on Wednesday, May 28, 2014 - 12:14 pm
Following my previous question, I learned that there are methods newly enabled in Mplus 7.2 for modeling skewed data. Based on what I understand from the slides available on Mplus website, I don't need to handle outliers in GMMs since the non-normal distributions will take care of them through adding and comparing results of different options of distribution (i.e., Skew-Normal, T, and Skew-T). Am I correct to conclude so about the new feature? Also in my dataset, skewness was up to 3.4 (not that severe, actually) but kurtosis seemed to be horribly high (around 8, on average). But I don't think the new feature of non-normal distributions in Mplus handles kurtosis, right?
 Bengt O. Muthen posted on Wednesday, May 28, 2014 - 2:25 pm
Mplus Version 7.2 handles non-normal distributions with both skewness and kurtosis. For instance, the t-distribution allows high kurtosis and the skew-t both.

You can also look for outliers using the Outlier option of loglikelihood (see UG index). Outliers may be present even when you use the new non-normal distributions.

These version 7.2 features will be taught at the IMPS 2014 meeting in Madison, Wisc this July - see the courses listed on the Mplus website.
 milan lee posted on Wednesday, May 28, 2014 - 2:48 pm
Hi Dr.Muthen,
Thanks for your reply! Just wanted to follow up your post, should I do anything about outliers before adding T and Skew-T distributions? Or just leave them unattended ?
Thank you!
 Bengt O. Muthen posted on Thursday, May 29, 2014 - 11:06 am
You can wait and look for outliers in the t- and skew-t runs.
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