First of all, thank you for the great updated lecture on the classical twin design! It was very helpful, and the way Hermine Maes confidently introduced the models’ syntax gives the hope that we can do it ourselves.
A couple of the questions on twin modelling that I would be happy to get opinion on.
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In CTD, when we compare the model fit, we are always looking into AIC (apart from the chi-squared statistics). Why don’t we compare BIC or check other model fit parameters commonly used in SEM?
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I know from the lecture that it’s common practice to choose the model with the lower AIC when the constrained model is not significantly worse than the unconstrained one. But should we somehow balance it with the degree of constraint as well? We have such an example on slide 28 for fitting the saturated model, where our lowest AIC is for model2, and it is slightly higher for model3, but we still conclude that the assumptions are met (probably because the difference is not significant). When we compare the fit of the ACE model, can we also choose the model that has a lower number of estimated parameters and is not significantly different from the less constrained model despite it has a slightly higher AIC?
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OpenMx is not happy when there are missing values in the definition variables, moderators, and the variables of interest themselves. Is there a way to deal with it, apart from restricting the sample or do imputation?
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When adding the covariates/ moderators to the model, to what degree is it crucial to add both linear and quadratic moderators? Can I skip the quadratic effect if I do not expect the quadratic effect on variance? Further, how do I make a decision if the effect on variances is quadratic or linear? As far as I understand, to examine the model with the quadratic effect on the variances (not means), I will need to respecify the model and fit it one more time with the qudratic effects on variances. I can then compare the model with linear effects on variances with the saturated model, and compare the model with quadratic effects on variances with the saturated model. Can I compare the fit of the model with quadratic effects on variances with the fit of the model with linear effects on variances to define which of them fits better, as they are not nested? Or would you maybe recommend to model both linear and quadratic effects for varainces in one model?
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I see in the literature that many articles specify the moderation models as moderated paths (with setting variances to 1). In the slides, I see you are doing it by adding a moderator to the var-cov matrices to the variances and specify accordingly in the figures. Just to confirm, it is recommended to do it like this, right?
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Lastly, does anyone have a link to an example script for the extended family design in OpenMx with twins’ parents that they can share (to start with)?
Thank you again for the inspiring lecture and your responses in advance!