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Equality Constraints

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jbauer's picture
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Joined: 04/14/2014 - 17:21
Equality Constraints

Hi Mike,

In my stage two analysis I would like to impose equality constraints on some items' error variances in the S matrix to be consistent with the models from the original studies.

I wonder whether this is feasible at all, because here (http://courses.nus.edu.sg/course/psycwlm/Internet/metaSEM/masem.html) you wrote "Since we are conducting a correlation structure analysis, the error variances are not free parameters."

If it is possible, could you please provide a syntax example how to implement the equality constraints?

Many thanks for your help!
Johannes

Mike Cheung's picture
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Joined: 10/08/2009 - 22:37
Hi Johannes, If a correlation

Hi Johannes,

If a correlation structure analysis is fitted, the diagonals of the model implied correlation matrix have to be fixed at 1; otherwise, it is not a correlation matrix. The error variances are not parameters if you specify "diag.constraints=FALSE" in tssem2() or wls(). The error variances can be "computed" after the analysis.

If you specify "diag.constraints=TRUE", the error variances are considered as parameters in the analysis. The diagonals are constrained by imposing nonlinear constraints.

In theory, you can impose equality constraints on the error variances by using the same label for the parameters. Please see the attached example. However, there may be some "unexpected" consequences. For example, I imposed the equality constraints on the error variances of the first and second variables (random2b). Since the diagonals of the model implied correlation matrix are always one, this means that the factor loadings of the first and second variables are also equal.

Alternatively, I fitted another model by imposing the equality constraint on the first and second factor loadings (random2c). This model is equivalent to the previous model in terms of fit indices and parameter estimates.

Regards,
Mike

jbauer's picture
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Joined: 04/14/2014 - 17:21
Hi Mike, many thanks for your

Hi Mike,

many thanks for your helpful response! I appreciate your efforts in maintaining this forum very much.

Is it correct if I assume that he "unexpected" consequences result because in tssem2() the equality constraints are imposed on standardized parameter estimates derived from a correlation matrix, unlike in "normal" SEM with raw data where they are imposed on the unstandardized estimates?

Best wishes
Johannes

Mike Cheung's picture
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Joined: 10/08/2009 - 22:37
Hi Johannes, Yes, it is due

Hi Johannes,

Yes, it is due to the differences on standardized versus unstandardized parameters. But I would that this is the "expected" consequences of analysis of correlation structure.

Regards,
Mike

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