I have just done the bivariate genetic model and I'm not sure about the accuracy of the results.

1. If Rg=-0.76, does this mean the genetic correlation between two traits is negative?

2. is there any relationship between the positive/negative of phenotypic correlation with that of Rg, Rc, or Re? If the phenotypic correlation between two traits is negative, are the Rg, Rc, and Re negative or any of the three can be positive?

Thank you

Hmm, a whole month, and nobody addressed this post. I'll give it a try.

1. Probably, yes, the genetic correlation is negative, but I can't say for sure without knowing which quantity is named "Rg" in your model.

2. If the phenotypic correlation is negative, I'm pretty sure it's possible for one or two of these correlations to be positive, as long as the three of them sum to a negative number sum to a negative number after being weighted by the products of the square roots of the two traits' corresponding variance proportions (see my post below).

I ran a 6 trait multivariate Cholesky decomposition based on Hermine Maes's scripts that were provided at one of the Twin workshops. I experienced the same problem when calculating genetic correlations based on the GenEpiHelperFunctions.R scripts provided.

Can the negative correlation be interpreted as the absolute correlation value, but with an opposite effect? So Trait1 and Trait3 have a strong correlation (0.7654), while high values of Trait1 cause low values of Trait2?

I also tried constraining all Path coefficients to be non-negative in the Cholesky model, which solved the negative correlation problem, but significantly decreased the fit of the model.

Thanks for your help!

This might help:

Source: Posthuma, D. (2009). Multivariate genetic analysis. In Kim, Y-K. (Ed.), Handbook of Behavior Genetics (pp. 47-59). New York: Springer Science+Business Media, LLC.

The genetic correlation doesn't have to be positive just because the phenotypic correlation is. A negative genetic correlation indicates that individuals with high genotypic values for one trait tend to have low genotypic values on the other.

You definitely don't want to "constrain all path coefficients to be positive". You might want to lbound at zero the diagonal of the 'a' matrix to rule out symmetrical ("flipped") solutions, but it's not typically necessary and can make computing CIs a hassle.

genetic correlation (Rg) is, I've found a much harder concept to explain and one that often leaves readers with the wrong idea (perhaps because it can be at or near 1 even when the traits in question have low or very different heritabilities). It's often more straightforward to explain things using the fitted model, rather than turn to Rg, where possible (sometimes that's what you want, but then be prepared to take care to explain things).

You certainly can get genetic correlations that differ in sign from the phenotypic correlations. And not just genetic correlations, but paths from shared latent genetic influences. This occurs due to countervailing environmental effects. It's unusual to find environments and genes that move distinct phenotypes in opposite directions, but interesting when it happens. Nurture, for instance might cause two traits to covary positively, while the underlying shared genetic influence causes them to covary negatively.

Be prepared for an uphill discussion with reviewers when you try and explain this :-)