Computing SE's: interaction of 2 stan... PreviousNext
Mplus Discussion > Structural Equation Modeling >
 Sharon Simonton posted on Tuesday, November 22, 2011 - 9:04 am
Dear Drs. Muthén,

I’m working on a study that’s using OLS regression models to assess the potential 2-way interaction of two standardized predictors on socioeconomic outcomes. We've manually standardized the variables and computed their product. I've read that a scaling adjustment is needed for the correct computation of the SE's for the interaction of 2 standardized predictors (article by Kris Preacher).

Does Mplus currently have an option/command for including such a scaling adjustment for the computation of the SE's? I also want to note that we're using imputed data sets (n =20) in case this is relevant here. Thank you for your help and all of the information on your website. Much appreciated!
 Bengt O. Muthen posted on Tuesday, November 22, 2011 - 9:38 am
Could you point to the article and page so I can see exactly what you mean?
 Sharon Simonton posted on Tuesday, November 22, 2011 - 10:37 am
Thank you for your response. The issue is described in section 5 of
"A primer on interaction effects in multiple linear regression"
on Kris Preacher's website(Vanderbilt University)at

I wrote Kris about it and he described the problem as:
"...the basic problem is that standardized variables always have a known variance of 1.0 by definition, whereas unstandardized variables have non-1.0 variances that vary from sample to sample. The "known" variance of 1.0 for standardized variables is really just masking the sampling variability in variances for our convenience without making it go away, but most software doesn't accommodate that fact. “

He wasn't sure whether Mplus has a way for accounting for this. The nature of our standardized measures makes it difficult to use the SE's computed using the unstandardized variables for significance testing. Thank you again.

Best wishes,
 Bengt O. Muthen posted on Tuesday, November 22, 2011 - 5:41 pm
A couple of points. When standardizing a coefficient, Mplus computes the SE of that standardized coefficients by taking into account the sampling variability in both of the two SDs involved in creating the standardization. For an interaction where standardized variables are used to create the interaction, I agree with Preacher that the SE of the standardized value is suspect. There is no way for software to know that the variables going into the interaction are already standardized. You could instead create the interaction based on variables that are centered but not standardized and (1) ignore the subtleties and use the SE for the standardized product coefficient as for any other variable, or more ambitiously (2) express the standardized values using Model Constraint and model parameter labels: We have a FAQ on how to compute the variance of a product - 3rd from the bottom at
 Sharon Simonton posted on Wednesday, November 23, 2011 - 10:08 am
Thank you so much for your response and the reference.

Best wishes,
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