Tests for overidentifying restrictions PreviousNext
Mplus Discussion > Structural Equation Modeling >
 Suyin Chang posted on Thursday, January 16, 2014 - 12:14 am
Dear Mplus community, I am new to Mplus, migrating from Stata and R's lavaan very recently. So forgive me if this question is fairly basic, but I was not able to find it out in the Guide so far.

What I am looking for is how to test for both the overidentifying restrictions and strength of instruments in Mplus.

Regarding the overidentifying restrictions tests, I am thinking of the approach of Sargan/Hausman'J tests for 2sls and 3sls, or even the Stata approach of performing the LR-test of the fitted model against the saturated model when using FIML.

It would be specially important if anyone know how to assess that, as well as maybe something like the strength of instruments, in the specific case of non-recursive models with clustered robust standard errors (clustering that I specified by passing type=complex and then informing in the code that cluster=clusteringvariable).

Any insights here will be very much appreciated.
Thanks for your time,

 Linda K. Muthen posted on Thursday, January 16, 2014 - 3:23 pm
The chi-square test of the H0 versus the H1 model is the test of overidentifying restrictions.

Mplus does not have an option for instrumental variables.
 Fabricio Vasselai posted on Thursday, January 16, 2014 - 8:21 pm
Regarding the assessment of instrumental variables, wouldn't it be possible to compare the fitted model against versions of this model specified with covariance between instruments and the error of the other equation? I mean:

- mainModel
model: Y1 on Y2 X1 X2
Y2 on Y1 X1 X3

- controlModel1
model: Y1 on Y2 X1 X2
Y2 on Y1 X1 X3
X2 with Y2

- controlModel2
model: Y1 on Y2 X1 X2
Y2 on Y1 X1 X3
X3 with Y1

And then compare main model against both control models through LR-tests or chi-square tests? If the main model is statistically different from all control models, then it would mean something similar to what Sargan/Hansen's J test.
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