Skewed quantitative variable in 3dLME?

AFNI Message Board
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Hi, I have a question for Gang.

I have a skewed quantitative variable I am trying to include in my model. The variable is a factor score from a CFA, and has a mean of 0.05, but it is very heavily skewed. Following are pictures of its boxplot and histogram. I am trying to model a dataset of twins, so I have to use 3dLME. I have two questions:

  1. Is 3dLME robust to violations of normality in quantitative variables? If not, what are some transformations we can do to the data in order to make it work?
  2. When we specified the CFA, we fixed means at 0 and residual variances at 1. Our thought initially was to specify the centering at 0. But given the skewness of this variable, should we be taking a different approach to thinking about centering?

https://i.imgur.com/EftlmdI.png
https://i.imgur.com/k3lX3Yb.png

Thank you very much!!

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The images don't show up properly on the message board for some reason.

Is 3dLME robust to violations of normality in quantitative variables? If not, what are some transformations we can do to the data in order to make it work?

From modeling perspective, there is no need to assume Gaussianity about the distribution of an explanatory variable (factor score in your case). Instead of the typical Gaussianity assumption is about the residuals and random effects in the model.

given the skewness of this variable, should we be taking a different approach to thinking about centering?

The center value is usually chosen for the convenience of interpretation. For example, at what factor score do you want to show the difference between two groups?