# Bivariate analysis: why best-fitting model's ACE estimates don't correspond well with the univariate estimates?

I have a question about bivariate cholesky ACE model. For model fitting, I compared the reduced models (selectively dropping a21, c21 and e21) to the full bivariate ACE model and the best-fitting model was selected based on lowest AIC and nonsignificant likelihood ratio chi-square test.

However, I noticed that the best-fitting modelâ€™s ACE estimates do not seem to match with what I obtained from fitting each of the two variables in univariate ACE models. For example, in univariate model fitting I got:

First trait: C = 60% (CI: 0.46-0.71) and E = 40% (CI: 0.29-0.54).

(Full ACE model: A = 5% (CI: NA-0.60), C = 55% (CI: 0.04-0.71), E = 39% (CI: 0.27-0.54))

Second trait: A = 82.6% (CI: 0.74-0.88) and E = 17.4% (CI: 0.12-0.26)

(Full ACE model: A = 72.4% (CI: 0.31-0.88), C = 10% (CI: 0-0.51), E = 17.4% (CI: 0.12-0.26))

The best fitting bivariate model for the two traits is ACE (drop c21 and e21) and the estimates are as follows:

confidence intervals:

lbound estimate ubound note

ACEnce21.SA[1,1] 1.261549e-01 0.2769508 0.6573700

ACEnce21.SA[2,2] 3.757661e-01 0.7011000 0.8840258

ACEnce21.SC[1,1] 3.156919e-02 0.3914759 0.5619521

ACEnce21.SC[2,2] 1.939172e-42 0.1306183 0.4428392

ACEnce21.SE[1,1] 2.354506e-01 0.3315733 0.4584370

ACEnce21.SE[2,2] 1.133622e-01 0.1682817 0.2513258

ACEnce21.rA[2,1] NA -1.0000000 -0.6036494 !!!

ACEnce21.corrA[1,1] -5.549520e-01 -0.4406475 -0.3113180

(Full BivACE model)

confidence intervals:

lbound estimate ubound note

BivACE.SA[1,1] 1.669727e-03 0.17771597 0.68945684

BivACE.SA[2,2] 2.799714e-01 0.66712995 0.88409716

BivACE.SC[1,1] 2.803414e-03 0.48075051 0.69603875

BivACE.SC[2,2] 2.393405e-43 0.16523408 0.54170390

BivACE.SE[1,1] 2.416883e-01 0.34153352 0.47200335

BivACE.SE[2,2] 1.122780e-01 0.16763597 0.25194368

BivACE.rA[2,1] NA -1.00000000 -0.99750231 !!!

BivACE.rC[2,1] -1.000000e+00 -0.24981942 1.00000000

BivACE.rE[2,1] -4.071271e-01 -0.17633429 0.06402325

BivACE.corrA[1,1] -6.319900e-01 -0.34432491 -0.02917323

BivACE.corrC[1,1] -3.865143e-01 -0.07041025 0.20042770

BivACE.corrE[1,1] -1.118121e-01 -0.04219267 0.01531362

As can be seen, the bivariate ACE estimates are rather different for trait 1 especially. In view of this, should I trust the ACE estimates yielded by the univariate ACE modelling more than the ones obtained from bivariate ACE modelling?

Besides that, the rA (genetic correlation) between the two traits appear to be -100%, which seems quite drastic. Can I actually put much weight on the results and interpret the findings accordingly?

Will greatly appreciate the input from the various OpenMx experts on this forum.

## Bivariate likely better

On the whole, I'd rather see results of full models - ACE or ADE than certain submodels. They are easier to incorporate into meta-analyses, apart from anything else.

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In reply to Bivariate likely better by neale

## the bivariate ACE estimates for trait 1 varied

Thank you very much for your advice. As I did bivariate modelling to compare trait 1 with 10 task measures, I noticed that the bivariate ACE estimates for trait 1 varied quite considerably when modeled with different task measures, with trait 1's A estimates varying from 11%-34%. I'm not quite sure how should I decide which of these estimates is more "accurate"? Could it be the one with the narrowest CI?

Another question I have is this: when I did bivariate full modelling for trait 1 and trait 2, trait 1's A estimate is 14% whereas trait 2's is 41%. When I looked at the squared standardized path a matrix, a22 squared is 0, which means that 0% of the genetic variance of trait 2 is due to specific gene action unrelated to trait 1's genetic variance. I find it quite hard to make sense of this, because given that trait 2's A estimate is considerably greater than trait 1, how is it possible that all its A estimate is shared with trait 1? If my genetic or environmental correlations' CI include 0, does it mean that these correlations are unreliable?

Thanks and best regards,

Yi Ting

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In reply to the bivariate ACE estimates for trait 1 varied by YiTan

## Good questions.

It is entirely possible for a factor to have greater effect on one trait than another. This is regularly observed in a factor analysis, in which loadings vary in size. Your data seem to be telling you that the same genetic factors affect both traits but do so with different effect sizes.

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