# Interpreting bivariate ACE output

Attachment | Size |
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Script for bivariate models | 22.52 KB |

"Confusing" output | 35.13 KB |

Hi all,

I am very new to genetic modelling and using ACE models. I have used Hermina's R script, slightly adapted to my question. I have having issues with the saturated models with constrained means (see other question I posted) but also in interpreting the ACE findings. First of all, in the ACE output I get negative A estimates which I would have thought would have been unexpected given the MZ/DZ correlations.

Secondly, I am not sure I get the output from the ACE model, is it the first column first row (of for example SA) indicating the proportion of variance explained by additive genetic factor in trait 1 (i.e., 0.17%) and the second row for trait 2 (1.9%)? However, I am not sure what the second row indicates. For example what is the SA=0.0283 indicating? The proportion of variance explained by additive genetic effect for the association between trait 1 and trait 2? Please find attached my script and my Ro file.

Any help in understanding why do I get these negative numbers and how to interpret these output would be appreciated. Thanks !

```
A A C C E E SA SA SC SC SE SE
US 0.0038 -0.0158 0.5092 0.2834 1.7550 0.5635 0.0017 -0.0190 0.2245 0.3410 0.7738 0.6780
US -0.0158 0.0655 0.2834 0.5856 0.5635 1.6622 -0.0190 0.0283 0.3410 0.2532 0.6780 0.7185
```

## Interpretation of estimates

Hi

Note that in this script the A C and E matrices are constructed from a Cholesky decomposition, by multiplying lower triangular matrix a by its transpose. That forces the A C and E matrices to be positive definite, which isn't ideal from a statistical point of view. See https://vipbg.vcu.edu/vipbg/Articles/PM30569348.pdf for why symmetric A C and E matrices that aren't constrained to be positive definite has statistical advantages.

In the SA columns the standardized estimates are arranged as a matrix, so .2245 and .2532 are the proportions of variation of A for the two traits, and -.0190 is the genetic correlation.

In the summary of the results, the diagonal of the matrix with columns A and A contains the estimated variance components for the two traits, and the -.0158 is the genetic covariance between the traits. The other contributions to the covariance, .5092 from C and .5635 from E are positive. Thus this is an example where the "bivariate heritability" idea fails. In general, I don't think bivariate heritability is a useful statistic because it isn't bounded between 0 and 1 if the contributions to covariation are of mixed signs. In this case it turns out negative. All that is quite OK, but the bivariate heritability is clearly a nonsense statistic. I generally prefer to consider the contributions to covariance without tacking on the term "heritability" since this is a proportion statistic that only works when all components have the same sign.

HTH!

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## Thanks for the paper. I was…

Thanks for the paper. I was aware of this issue - from this blog and that exact paper. However, I became aware of this after pre-registering the analyses plan. We discussed to use the variance based models instead but the idea for now I think would be to fit this only as sensitivity analysis and check that we are indeed getting the same results to the Cholesky.

Regarding your response:

Thus this is an example where the "bivariate heritability" idea fails. In general, I don't think bivariate heritability is a useful statistic because it isn't bounded between 0 and 1 if the contributions to covariation are of mixed signs. In this case it turns out negative. All that is quite OK, but the bivariate heritability is clearly a nonsense statistic. I generally prefer to consider the contributions to covariance without tacking on the term "heritability" since this is a proportion statistic that only works when all components have the same sign.

Sorry if I am being slow to understand this. I am trying to use this paper to better interpret this output.

Do you then mean that in my example -0.0158 is the genetic covariance (bivariate heritability) and -0.0190 is the genetic correlation (which are then distinct concepts?) ?

Thanks again for all your help with this!

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In reply to Thanks for the paper. I was… by Ilaria

## Yes and no

Yes, -0.0158 is the genetic covariance estimate (but no it is not the bivariate heritability, that statistic is nonexistent/nonsensical here due to different signs among the three contributions to covariance) and -0.0190 is the genetic correlation estimate.

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## Hi, Just following up on…

Hi,

Just following up on this and whether someone knows whether I am getting this distinction right from my data. Also how likely is that the values are indeed negative?

Thanks a lot!

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