So it seems to me that there are two key things one should do if one wants an unbiased use (/estimates) of the ACE model. One is making sure the classical twin design assumptions are met (e.g. variances equal across groups), etc. I am wondering, on top of this, should normality be explicitly tested for as well? I had read that if the assumptions needed in general for a classical twin design (those relating to mean and variance equality) are violated, that then that would then indicate the data is potentially nonnormal. But, if all the assumptions are satisfied, does that necessarily mean that the data are necessarily normal 'enough' for the ACE model? Or should that also be explicitly tested for using some normality test (even if the variables are fisher-z transformed and all other assumptions are met successfully)?

I appreciate it!

In general we cannot assume that the assumptions of the ACE have been met, because many of them are empirical questions, say if we measure Gs and Es and observe their covariance is close to zero, then there is some empirical support for the hypothesis that there is no G-E covariance, but that isn't proof. So, in general, no, the twin model assumptions are not sufficient as a test of normality. Again, however, they can provide support for the hypothesis that the data are consistent with multivariate normality (departures will tend to cause the saturated model to fit a lot better than one where twin covariances & means are constrained equal across twin 1 and twin 2), but it seems better to test MVN directly with Kolmogorov-Smirnoff test or similar.

Note also that if there are ordinal level of measurement data, they should be analyzed as ordinal by, e.g., integrating over the multivariate normal done semi-automatically in OpenMx with ordinal (ordered factor) variables. You need to provide a model for the thresholds in this case. WLS provides an alternative fit function that is less restrictive - elliptical is required but normality is not.

Thanks a lot AdminNeale! That's definitely interesting and does makes sense.

So I guess it makes sense to test for all of these entirely in that case.

I guess that only raises one question for now--if the concern is for multivariate normality, then, do we care about normality involving twin 1 and twin 2 separately in a given population (specifically a multivariate normality test, as opposed to a single normality test on just the population of all MZ twins for the given phenotype, etc.)?

As for ordinal methods: I am thinking of excluding the nonnormal/violating assumption phenotypes of interest for consistency, but maybe will also look into ordinal methods at some point and that's definitely a useful reference point.

I came across another post in the forums which cites: https://www.dilipmutum.com/2011/07/normality-issues-in-sem.html

to say that in general nonnormality isn't as clear of an issue in these kinds of studies? I would wonder at what point a cut-off of too 'nonnormal' (bivariate nonnormal specifically as it involves both twins) would be if you are assessing it using any kind of multviariate normal test.

I was wondering, in the case of nonnormality (but success with regards to the actual core ACE model assumptions), would what AdminRobK said back here still old as an alternative (imxRobustSE)? And if so, is this the native implementation when someone generates confidence intervals in umx (like in umxConfint) or openmx in general? https://openmx.ssri.psu.edu/comment/7177#comment-7177