Multigroup SEM - comparing path coefficients across groups

[HSchw]

Hello, 

I'm analysing a multigroup SEM. I achieved strong invariance regarding gender. 

Now I'm interested in one path. I see the path coefficient of boys is different to girls. Now I want to compare these two coefficients across groups (i.e. like mean differences) and analyse if the difference between this two groups is significant. Is it possible to obtain the p-Value / Wald-z Statistik from the R output or do I have to calculate another model?

Or do I have to do a moderator analysis in the total group and adding gender as a variable to my model. But I don't really understand how to do a moderator analysis in R. 

Thank you!

[Terrence Jorgensen]

Is it possible to obtain the p-Value / Wald-z Statistik from the R output

Yes, if you define a new parameter as the difference between those parameters.  This is similar to defining indirect effects as products of individual paths:

http://lavaan.ugent.be/tutorial/mediation.html

You could also constrain the paths to equality across groups by giving them the same label, then comparing that restricted model to the model without the restriction, using the lavTestLRT() function.

http://lavaan.ugent.be/tutorial/groups.html

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

[ces...@ucsc.edu]

Hi Terrence,

Thank you for this answer! If I'm reporting the difference between those 2 parameters, do I report the z score, or the estimate? (Also, what kind of estimate is it?)

Thank you,

Christy

[Terrence Jorgensen]

If I'm reporting the difference between those 2 parameters, do I report the z score, or the estimate?

Both, assuming you want to test the null hypothesis that the difference is 0 in the population.

(Also, what kind of estimate is it?)

I don't understand your question.  If you use ML estimation, it is a ML estimate.  It is a difference between 2 parameters, as you said (which might be described another way depending on what the 2 parameters are).

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[ces...@ucsc.edu]

Hi Dr. Jorgensen,

Thank you!!

By what kind of estimate, I mean, how do you report it? For example, with a z score, I would write z = [number]. Do I just write estimate = [number]? For reference, it's student's unstandardized math identity scores. 

Also, thank you for answering so many of our questions!! I hope you get tenure soon, you deserve it :-)

Christy

[Terrence Jorgensen]

how do you report it? For example, with a z score, I would write z = [number]. Do I just write estimate = [number]? 

Both.  It is a regression slope, so you can use that format:

b = <unstandardized estimate>, 95% CI [lower, upper], β = <standardized estimate>, z = <Wald z statistic>, p = ...

[ces...@ucsc.edu]

Thank you!!