Can you explain the comparison of the saturated to the ACE model again?
The saturated model is the best possible model. The ACE model is a candidate you’re interested in. The comparison asks “Do these two models fit about the same?”. If they do, then the simpler model (i.e., the ACE model) is preferred.
A saturated model in this context (i.e. univariate data from the classical twin design) means that we estimate different means, variances and covariances for each individual in the study. In other words if we have MZ pairs and DZ pairs, there are different means for MZ twin 1, MZ twin 2, DZ twin 1, DZ twin 2; Different variances for MZ twin 1, MZ twin 2, DZ twin 1, DZ twin 2, and of course difference covariances between MZ and DZ pairs. That’s 10 free parameters. When we fit an ACE model, all the variances become equal to A+C+E, so instead of having 4 different variances, we now have one variance for everyone. We may also decide to constrain the means equal, so instead of having 4 different means, we now have one mean for everyone. We would now be estimating 4 parameters in total: A, C and E and 1 mean for everyone. 10 - 4 = 6 degrees of freedom test.
I haven’t considered sex of the twins in the above.
Dave
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