Bayes analysis for multilevel SEM PreviousNext
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 Marina Milyavskaya posted on Tuesday, July 05, 2016 - 10:23 am
I am runing a multilevel SEM analysis, and hypothesize that one of my parameters is equal to 0 (i.e., want to confirm the null). I know that this is something that can be done with Bayesian analysis, but am unclear how to actually do it with Mplus & the output that I get when I run the model using bayes estimator. I have read some materials looking at BSEM & ascertaining model fit, but nothing about testing a specific parameter as equal to 0 (rather than different from 0).
Is there a way to obtain a Bayes Factor for testing a parameter against a specific value? Or am I supposed to compare models where the parameter of interest is free vs. constrained to 0?
Thank you!
 Bengt O. Muthen posted on Tuesday, July 05, 2016 - 6:08 pm
Why not just look at the Bayes 95% credibility interval for this parameter when it is allowed to be free and see if this interval covers zero? If it does, then in frequentist terms you cannot reject that the parameter is zero.
 Marina Milyavskaya posted on Wednesday, July 06, 2016 - 2:32 pm
I don't want to just 'not reject' that the parameter is zero, but figure out how likely it is that this parameter IS zero.
So if I had competing hypotheses (that x=0 vs. x > zero), how strongly does the data support the hypothesis that x=0?
 Bengt O. Muthen posted on Wednesday, July 06, 2016 - 5:55 pm
The p-value you get from the Bayes output will tell you -

for a positive estimate: how likely is it that the parameter is negative

for a negative estimate: how likely is it that the parameter is positive

I don't know off-hand how a Bayes factor test would look here.
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