Model to base comparisons on for chi-square goodness-of-fit?

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Karin's picture
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Joined: 02/11/2011

I fitting twins data and comparing an ACE model (say) to the fully saturated model, using the chi-square from this as a measure of goodness-of-fit.

I have ten parameters in the fully saturated model (2 x 3 covariance parameters and 2 x 2 mean parameters) and four in the ACE model (a,c & e plus overall mean), so am comparing to a chi(6).

I am worried that in comparing this models as a goodness-of-fit test I am to some extent testing whether an overall mean should be fitted (as distinct from MZ mean 1, MZ mean 2, DZ mean 1, DZ mean 2) rather than just whether the ACE model is a good fit.

Would it be better to test whether the means can be equated and, if so, equate them and compare the difference in deviance between a fully-saturated-apart-from-means model with seven parameters and the four-parameter ACE model to a chi(3)?

Thankyou

Karin

mhunter's picture
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Joined: 07/31/2009
I think you suggest a good

I think you suggest a good strategy. If you're concerned that the means may be different, then test if you can equate them.

The saturated model vs ACE model comparison will only tell you if the fit of the ACE model is distinguishable from the free-est, best-fitting model. It will not tell you WHERE the difference is, assuming there is one.

You could compare the ACE model to a "saturated" model where the means have been equated. In general, any nested models can be compared. The OpenMx function mxCompare() should help with this.

Karin's picture
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Joined: 02/11/2011
Thanks!

Many thanks for your helpful reply. It's good to know that I am not barking up the wrong tree...
Karin