I'm running a simple ACE model of a continuous variable in openMX. I'm running both a constrained and sex-limited model to see which provides a better fit, and then running various constrained or sex-limited submodels where a or c are dropped.

Here is what I have noticed -- in a sex-limited submodel where c is dropped, the a and e variance components and confidence intervals are extremely similar across males and females -- AND, extremely similar to the components for a constrained model where c is dropped.

However, the sex-limited model is a SIGNIFICANTLY better fit. There is no comparison. It's waaaaay better, and yet, in reporting the variance components, it looks like it's about equal to the constrained model that's more parsimonious.

I'm having trouble wrapping my mind around this conceptually. Anyone have any insights? Would it be helpful to post my syntax?

The models'

`summary()`

output would probably be more informative, though the syntax might be helpful, too. If you post them, attach them to your post as text files, or at least use the`<code>`

HTML tags if you include them in the body of your post.I do apologize for the delay - this is still a question I'm interested in. I've attached a textfile with the actual syntax for my models. In the body of my post are the summaries for my models:

twinACE2 = constrained across gender, full ACE

TwinAe2 = constrained across gender, drop C

twinACE3 = sex limited, full ACE

TwinAe3 = sex limited, drop C in both males and females

I also included a mxCompare for the TwinAe2Sum and the TwinAe3Sum, where TwinAe2 is much worse despite very similar estimates for the variance components.

I think the explanation is that the raw variance components are simply larger for males than for females, to the degree that equating them to be equal induces substantial misfit. If you look at the point estimates from the sex-limited AE model, then (I'm assuming a single phenotype) the additive-genetic variance for males would be about 0.84^2 = 0.71, and the nonshared-environmental variance for males would be about 0.78^2 = 0.61. But for females, additive-genetic variance would be about 0.57^2 = 0.32 and the nonshared-environmental variance would be about 0.56^2 = 0.31.

On the other hand, the standardized variance components (the variance proportions) do appear to be similar for both sexes. For instance, in the sex-limited AE model, males would have a narrow-sense heritability of about 0.71/(0.71+0.61) = 0.54, and females would have a narrow-sense heritability of about 0.32/(0.32+0.31) = 0.51, which (allowing for rounding error) are close to the point estimates of your MxAlgebras, displayed in the output for the confidence intervals.

So, the standardized variance components are similar by sex, but the raw variance components differ by sex; in other words, heritability is similar by sex, but males have greater overall phenotypic variance.

BTW, I notice that your

`summary()`

output says you're using OpenMx version 1.4-3060. Does`mxVersion()`

also say you have version 1.4-3060, and if so, are you using R version 3.1.0 or later? If yes, you should DEFINITELY upgrade your version of OpenMx to version 1.4-3475, or better yet, version 2.0 or 2.0.1. There's a reason we have a yellow-highlighted warning about this on the front page of the OpenMx website.Ah, I see! Thank you for this very cogent explanation!

Yes, I recently noticed this warning, and much appreciate the heads up. I noticed this yesterday and I think I'm using R 3.0.3 -- that should mean that my output is okay, right? But I need to go ahead and upgrade both OpenMX and R to the latest versions. (Does Open Mx 2.0 run with versoins of R lower than 3.1?)

If you're using OpenMx 1.4-3060 with R 3.0.3, you should be fine. If you want to upgrade to OpenMx 2.0.x, you'll be able to, since it's compatible with (I think) R 3.0.2 and later.

Ah, thank you! Looks like we were typing replies at the same time.

A follow-up question as I contemplate on this: is it clearly correct to say that it would be better to present a univariate ACE model where gender isn't addressed at all rather than a constrained one that is substantially misfit? I think the answer would be clearly yes. And then would it be fair to say that it's not as unequivocally better to present a sex-limited ACE than a univarate ACE that doesn't address gender at all? Unlike a constrained model with a very poor fit, it's not that the narrow-sense heritability estimates in this generic univariate ACE should be questioned or that they necessarily disproportionately reflect one gender over another, but just that they don't tell the whole story of what's going on in the background compared to the sex-limited.

(Just thinking about how to make analytic plans in the future.)

It is possible to fit a model that specifies the same proportions of variance, but a different total variance for the two sexes. Notation got scrambled at some point (possibly my fault) but this has been called a scalar sex difference model. Let's call it a variance difference model. To implement it, I would constrain am=af cm=cf and em=ef, and add a diagonal matrix with starting values equal to one. We only want to scale twin 1 in the OS DZ group if Twin 1 is male, so we need two matrices to "wrap" (i.e., pre and post-multiply) the previous expected covariance matrix with using the quadratic %&% operator. Something like

In a multivariate analysis, we'd probably want to do this a bit differently to simplify specification, e.g., using a diag(2) matrix to Kronecker product the variance differences matrices.

There don't appear to be OS DZ twins in this case. It would be pretty simple to re-parameterize the model in terms of standardized variance components (constrained equal across sexes) and raw phenotypic variance or SD (allowed to differ by sex).

Edit: Something like my suggestion in another thread.

Thank you for these extremely helpful insights! I didn't see your comment until after I saw Dr. Neale's. I updated my code to reflect his suggestions. My sample indeed does not have opposite sex twin pairs, so I modified it for the bivariate case.

It looks to me like the output is as it is supposed to! The raw variance is different across gender but the standardized variance components are the same. I've attached my output here just to confirm that I've put these suggestions into place correctly. (Note that I used a different variable which is why the results are way different than my original post.) Thanks again!

Good to hear. You're welcome.

I don't think I understand your question. What do you mean by "gender isn't addressed at all" and "doesn't address gender at all?"