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Mplus Discussion > Structural Equation Modeling >
 John Venz posted on Friday, April 29, 2016 - 9:10 am
Dear Mr. and Mrs. Muthen,
I ran the follwoing SEM model including only continuous variables, and one second-order latent factor:

f1 BY i1 i2 i3;
f2 BY i4 i5 i6;
f3 BY i7 i8 i9;
Gen BY f1 f2 f3;


Out ON Ind Gen f1res f2res f3res;

where Out and Ind are observed variables and f1res, f2res, f3res are the residuals corresponding to f1, f2, f3 constructed according to Mplus FAQ "Regressing on a residual".
According to the output I got and to my own thougts, this model seems not identified. However, if I define Type=Random and add Interaction Terms to the model,

IndxGen | Ind XWITH Gen;
Indxf1res | Ind XWITH f1res;
Out ON Ind Gen f1res f2res f3res;
Out ON IndxGen Indxf1res;

then the model terminates fine with no problems at all and the results do make sense. However, I am wondering how trustworthy the results are if the 'main effects model' is not even identified.

Could you give a hint/reference, both intuitively and mathematically, how this is possible? Furthermore, do the results from the 'interacton model' make sense from a statistical viewpoint?(or are they unstable, probably not replicable?)

Alls this occurs if both analysis (the ones with and without interactions) are done with TYPE=RANDOM, ALGORITHM=INTEGRATION, ESTIMATOR=MLR.

Thank you very much.
 Bengt O. Muthen posted on Saturday, April 30, 2016 - 6:07 am
I would first figure out why the main effects model is not identified. Make sure that your residual factors are specified as uncorrelated with the other factors for instance.
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