Robust statistics in CFA (or SEM) output with "WLSM" estimator

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Павел Валединский

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Feb 9, 2020, 12:04:11 PM2/9/20
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Hi everyone!
Now I'm trying to run SEM (and CFA) models with categorical predictors (factor indicators) and categorical outcomes (dependent variable), all have non-normal distibution. When I run "cfa" (or "sem") fuction with "WLSM" estimator, two columns appear in the output instead of one (as it is with default "ML" estimator). 
So tell me please what this second "robust" column stands for??
Thank you!
Robust stat.PNG

Terrence Jorgensen

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Feb 11, 2020, 6:57:09 AM2/11/20
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I'm trying to run SEM (and CFA) models with categorical predictors (factor indicators)

Indicators of common factors are outcomes, not predictors.  The common factor is the explanatory variable.
 
all have non-normal distribution.

That is true by definition :-)  Normal variables are continuous, not categorical.
 
When I run "cfa" (or "sem") fuction with "WLSM" estimator

It should be WLSMV by default.  WLSM is insufficient for this scenario.
 
two columns appear in the output instead of one (as it is with default "ML" estimator). 
So tell me please what this second "robust" column stands for??

The robust column is the one that you want to pay attention to.  It means what it says: the statistics are robust to the violated assumptions of the statistics in the "Standard" column, so the Robust column's statistics have Type I error rates that are closer to the nominal values.

Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam

 
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