Are there situations where using a ACE(/ADE) mdoel with sex as a covariate would make more sense than a sex-difference ACE(/ADE) model?

Thanks for the question Rebecca! The short answer, is â€śnot reallyâ€ť. Adding a covariate is accounting for the role of sex on the means and as such will not change the variances . Sex difference ACE/ADE is focused on understanding the role of sex on the variances by sex. If there is a sex difference on the means, there is likely a sex difference on the variances.

Hi - I agree with Lizâ€™s response but wonder if the following would help further. Another way to think about sex as covariate vs. sex-limitation model is as the difference between fixed and random effects. In SEM, the triangles are for modeling means, and mean differences can be specified as different parameters for, say, males and females. Correcting for a mean difference can be thought of as starting with data that follow two normal distributions with some difference (say 2-3 SDs to make it obvious in a plot). Including sex as a covariate (which can also be regarded as moderating the mean parameter by sex) puts the two distributions on top of each other. However, having done so, the distributions might still differ by variance. Allowing different variance parameters for the two groups effectively removes (or models really) the variance difference. Since weâ€™re looking at sources of variation in the samples, you can think of this as a random effect.

I am working on twin data (facial and dental measurements) of around 200 twin pairs, including DZOS twins. Is it worthwhile to run a sex-limited univariate ACE/ADE model if the correlation of DZOS twins is comparatively lower than the correlations among DZ (same-sexed) twins, considering the sample size is not large enough?