Hi Statalisters,

I am trying to do a SEM on my data (SEM was chosen because my hypothesis involves testing mediating effect of a variable). However, the variables of interest do not meet the multivariate normality assumption. I am seeking advice and help on how I can transform the variables so that they are normally distributed.

I will list 3 of the variables of interest as an example here (the data is longitudinal in nature, the total N of observations =9,525):
v1: Number of total social interactions one reports in a day that involve having a meal together. M=0.57, SD=0.84. It has a lot of 0 values because not all social interactions involve sharing a meal. The histogram of the variables looks like this:
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v2: Positive interaction score. it’s a daily average of people’s ratings of how positive each interaction they have in a day. The scale is from 0 to 10. M=7.70, SD=2.28, the histogram is below:
Array

v3: Depression score. This score measures people’s daily depressive symptoms on a scale of 0 to 8. M=1.44, SD=2.00. the histogram of the variable look like this:
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The SEM I want to build looks something to this:
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However, since none of the variables is normally distributed, how can I transform the variables such that I can work with SEM? I have tried the gladder command. However, none of the transformations resolve the non-normality issue.

Thank you very much in advance for your help and feedback! If there’s anything I am missing or not clear on, I'd be more than happy to clarify.

Siyan