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Bivariate Cholesky Decomposition Model - Negative Unique Environment Estimate

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No user picture. bjoyner Joined: 01/28/2022
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Behavioral Genetics Models
Hello, all!

I am attempting to examine the covariance between two variables (callous, vict3_cfa) using a bivariate cholesky decomposition model. However, when I run the models, the unique environment estimate for the best fitting model comes out as negative.

I have read up on this topic quite a bit and I am at a lost as to why I am continuing to get a negative estimate. I have ran the model as only containing (1) twins, (2) twins and full siblings, (3) twins, full, and half siblings, and (4) twins, full, half, and non-related siblings and every time I receive a negative estimate in the unique environment. If someone could explain to me why this is happening that would be great!

Thank you all in advance for your help!

Replied on Thu, 02/17/2022 - 16:49
No user picture. bjoyner Joined: 01/28/2022

Absolutely!

**Model with Twins Only**
*AE Covariance Matrices & Proportions of Variance Matrices*
[1] "Matrix A"
covA1 covA2
callous 7.9439 0.4405
vict3_cfa 0.4405 0.0955

[1] "Matrix E"
covE1 covE2
callous 9.4519 - 0.1281
vict3_cfa -0.1281 0.5233

[1] "Matrix V"
var1 var2
callous 17.3958 0.3124
vict3_cfa 0.3124 0.6188

[1] "Matrix A/V"
stcovA1 stcovA2
callous 0.4567 1.4101
vict3_cfa 1.4101 0.1543

[1] "Matrix E/V"
stcovE1 stcovE2
callous 0.5433 -0.4101
vict3_cfa -0.4101 0.8457

*AE Correlation Matrices*
[1] "Matrix solve(sqrt(I*A))%&%A"
corA1 corA2
callous 1.0000 0.5058
vict3_cfa 0.5058 1.0000

[1] "Matrix solve(sqrt(I*E))%&%E"
corE1 corE2
callous 1.0000 -0.0576
vict3_cfa -0.0576 1.0000

File attachments
twoACEvc_threshold_vict3.pdf
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Replied on Sun, 02/20/2022 - 16:31
No user picture. bjoyner Joined: 01/28/2022

I get the same negative estimate using umxACEv as well.
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Replied on Mon, 02/21/2022 - 10:13
No user picture. bjoyner Joined: 01/28/2022

Hello! I guess I misunderstand then as I understand the results to be the proportion of the covariance due to the additive genetic and non-shared environment influences. With the non-shared environment being negative, that causes the additive genetic estimate to be over 1. How would I then interpret these results?
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Replied on Mon, 02/21/2022 - 15:31
Picture of user. AdminRobK Joined: 01/24/2014

Hello! I guess I misunderstand then as I understand the results to be the proportion of the covariance due to the additive genetic and non-shared environment influences. With the non-shared environment being negative, that causes the additive genetic estimate to be over 1. How would I then interpret these results?

Interpreting the off-diagonal elements of `A/V` and `E/V` as proportions only makes sense if the additive and nonshared-environmental covariances are both positive. They don't really have a simple interpretation if one of those covariances is negative.

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Replied on Tue, 02/22/2022 - 10:02
Picture of user. AdminNeale Joined: 03/01/2013

Hi Bridget

Unforntunately, this happens quite often with proportions of covariance. It is why the "Bivariate Heritability" statistic touted by some purveyors of Behavior Genetics is basically rubbish. Even when ra, rc and re are all positive, it still isn't a good statistic because of the lack of -1 to +1 bounds that are implicit in taking a proportion (the boundaries of the non-proportion ra/(ra+rc+re) are not +1 and -1 so it is a misleading statistic even in the cases where it "works." So we need a less simple interpretation.

I prefer to consider the contributions to the covariance without doing any division. Simply state the phenotypic correlation is comprised of ra, rc and re, whose values are x, y and z, respectively. Anything else seems disproportionate :)

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