Testing assumptions for expected siblings’ covariances

Hi. Inspired by the conversation of today and by the lecture of yesterday, I tried to figure out whether it was reasonable to assume, within the simulated dataset, the assumption that covariances between DZ and Siblings are the same.

I thought that a nice way to test for it is to extend the saturated model to include siblings. (note: this might be a bit dull, as I can imagine becoming a bit cumbersome with an increased number of twins; nevertheless, I guess it might work as a proof of concept)

In words, the extended saturated look a bit like this:

Constrain expected Means to be equal across Twin Order

Constrain expected Means to be equal across Sibship Type (i.e., sibling in the correspondent Zygosity group)

Constrain expected Means and Variances to be equal across Twin Order and Sibship Type

Constrain expected Means and Variances to be equal across Twin Order, Sibship Type and Zygosity

Constrain expected covariances across Sibship Type within Zygosity

Constrain expected covariances across Sibship Type within and between Zygosity

Constrain expected covariances between Sibship Type and Dyzgosity to be equal

I might have made some mistakes along the way, but if not, then it looks that the assumption is not too reasonable (?); in this particular case, it looks like points 6 and 7 significantly decrease the model fit (e.g., the covariance between Sib and MZ is higher than between Sib and DZ.)

I would love to hear some opinions. I am thinking about including siblings soon in one of my PhD projects, and I wondered if the approach outlined above is a feasible way to proceed before fitting an ac(d)e model.

I created and stored a reproducible example in

home/giacob15/day2/saturated_sib.R