# Help with thinking about a non-trivial GxE twin model

On a phenotypic level, I'm testing a model where Trait1 is moderating the effect of environment on Trait2.

However, when wanting to test my model within a genetic level, I'm having trouble to figure out what model I can use that will be most similar to the claim I have within the phenotypic level.

I can test whether my environmental factor moderates the genetic effects of Trait2 (with a GxE twin model). But this misses the part where Trait1 (which is highly heritable), moderates the association (or maybe the moderation?).

I'm familiar mainly with basic ACE models (multivariate, sex-limitation, basic GxE), so I have no idea if there's an option to build a model more suitable for my hypothesis, or even what such a model looks like.

I would appreciate any thoughts or ideas on the matter,

Thanks!

Noam

## umxGxEbiv

Purcell, S. (2002). Variance components models for gene-environment interaction in twin analysis. Twin Research, 6, 554-571. doi: [10.1375/twin.5.6.554](https://doi.org/10.1375/twin.5.6.554)

van der Sluis, S., Posthuma, D., & Dolan, C. V. (2012). A note on false positives and power in G x E modelling of twin data. Behavior Genetics, 42, 170-186. doi:[10.1007/s10519-011-9480-3](https://doi.org/10.1007/s10519-011-9480-3).

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In reply to umxGxEbiv by tbates

## Can it include a third variable?

However, I have a third variable, but I didn't see that the model can accommodate a third variable - is there such a possibility?

At the moment the only idea I had is to take my phenotypic moderator and split by it the sample into two groups (high and low), and test whether the estimations of umxGxEbiv differ between these two groups (that is, whether the moderating effect of E on G, differ by levels of M). If there a way to incorporate this third variable in the model without dichomitization?

Thanks!

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In reply to Can it include a third variable? by noamm

## Correction

And if so, does it matter that the dependent variable is skewed?

Thanks again

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In reply to Correction by noamm

## comments

The content in this other thread might be helpful to you.

It won't matter for estimation purposes, but if the skew is nontrivial, it might matter for statistical-inferential purposes. However, is the variable skewed once you condition on covariates? That's what really matters.

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In reply to comments by AdminRobK

## How to implement

Thanks for the referral to the three-way interaction thread.

To clarify, I have a phenotype of interest and 2 continuous moderators, but what really interests me is the moderation effect of the interaction term between these moderators on the phenotype of interest. I saw in the Purcell paper that the model can allow such estimations.

In the three way interaction thread you referred me to, you wrote in the last comment:

"What I'd suggest instead is a "full bivariate" analysis of birth weight and the ordinal trait. In this model, each moderated path coefficient will have the form of

a + b*x + c*y + d*x*y

where 'x' is birth weight, 'y' is parental education, 'a' is the "unmoderated" coefficient, 'b' is the coefficient for birth weight, 'c' is the coefficient for parental education, and 'd' is the coefficient for the product of birth weight and parental education. Be sure to include parental education as a covariate for both birth weight and the ordinal DV."

This is exactly what I want, but instead of the second moderator being a covariate (there it is shared between twins), I want it to be another phenotype of interest like the birth weight in this example (which is not shared between the twins).

The thing is, from the Purcell paper I can't seem to understand how the beta's are calculated (they are simulated), so I can't figure out how to implement your suggestion.

Up until now I used the umx package because I'm not familiar enough with the OpenMx language, but umxGxEbiv only accepts one moderator. I hope that if I'll understand how the betas are calculated I could implement it based on a multivariate umx model.

Thanks!

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