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# Sex Limitation Model Question

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Joined: 10/18/2018 - 13:26
Sex Limitation Model Question

Hi,
I attended the Boulder workshop a couple years ago and am now trying my hand at sex limitation modeling. Currently, I am working on a same-sex twin pair sex limitation model for liability to alcohol use disorder. I've found measurement invariance and A and C are invariant. C was non-sig. and is constrained to zero. The AUD factor intercept is invariant. Can I interpret the sex difference in the AUD means in terms of greater genetic risk for AUD in the males?

I've done some reading, checked out the OpenMX forum, and looked back at the Boulder slides (they mention mean differences but then move quickly to scalar and non-scalar limitation). I'm guessing this is so basic that I'm not seeing the answer somewhere....

Thanks for considering my question!
George

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Joined: 03/01/2013 - 14:09
Not really

Differences in means, which can be tested statistically within the model, may be interpreted as, e.g., greater risk for males than females. However, attributing the risk to greater genetic factors isn't possible in most cases, because either or both sources could be responsible (and perhaps not in the same direction). Sure, if 99.9% of variance was genetic, and there was a substantial mean difference, it would be almost certain that mean differences arise from this source. One could explore just how different the environments (e.g.) would have to be for males and females in order for the mean difference to stem entirely from that source. In the example I just gave, a very (implausibly perhaps) large environmental effect size on the means would be necessary to generate the observed differences, mainly because the difference would be multiplied by the path coefficient from latent E to phenotype.

In a multivariate context, some more leverage can be obtained, and factor means may be identifiable parameters given certain assumptions. Conor Dolan investigated this in the context of race differences in intelligence (https://www.tandfonline.com/doi/pdf/10.1207/S15327906MBR3501_2)

HTH!
Mike

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Joined: 10/18/2018 - 13:26
Thanks and could I trouble you a little more? :-)

Thanks, Mike! I think maybe I should not have said "interpret the sex difference." I didn't mean to suggest I was thinking it was largely or wholly due to A. In the case that there is a factor mean difference on latent AUD by sex, strict invariance holds, X has an effect on latent AUD, and the AUD factor intercept is invariant, I thought I could say that some of the mean difference on AUD is likely attributable to X. I imagine it would even be possible to pool the groups and estimate the indirect effect of sex --> X --> AUD, to get a sense of how much of the difference is attributable to X. Am I off base here? This is the kind of thinking I'm doing when testing invariance of a measure and making inferences about whether item mean differences are attributable to latent mean differences. But maybe here the proximate cause assumption doesn't hold so the potential for confounding is, in theory, too great? And that's why we can only do some sensitivity analyses such as those you suggested?

The Dolan paper looks really helpful though I'm not sure I want to get into competing models of AUD quite yet. Am I right that this is mostly attending to measurement structure differences (i.e., g vs. non-g models)?

Thanks again for your time! I can't quite seem to get around this conceptual roadblock on my own.

• George
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Joined: 10/18/2018 - 13:26
Also...

In your last sentence did you mean ACE factor means?

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Joined: 10/18/2018 - 13:26
Ah answered that last question myself.

.