# Multivariate ACE Vs. Multilevel Model

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George Richardson
Joined: 10/18/2018

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Hi All,

I'm trying to understand the relationship between multivariate ACE models (e.g., Cholesky model fit to two phenotypes) and multilevel behavior genetic models. Is there a formal comparison somewhere?

I'm trying to understand the relationship between multivariate ACE models (e.g., Cholesky model fit to two phenotypes) and multilevel behavior genetic models. Is there a formal comparison somewhere?

My sense is that multivariate ACE models conflate within and between pair variance. A and C could capture within and between effects while E captures the within pair effects. E will map right onto the within pair effect in the multilevel model (MLM). Is all this correct?

I think A and C are estimated at the within pair level in the MLM, though I saw one paper in which it looked like they were estimated at both levels. Is this correct? And, how does C estimated from a multivariate ACE model relate to the twin pair level deviance from the population mean in the MLM? I don't think they are equal but am not sure.

Any help is greatly appreciated!

-George

## Same model, different specification

*Verhulst, B., Prom-Wormley, E., Keller, M., Medland, S., Neale, M.C. (2019). Type I Error Rates and Parameter Bias in Multivariate Behavioral Genetic Models. Behav Genet. 49(1):99-111.

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In reply to Same model, different specification by AdminNeale

## One follow up question about twin pair means

BTW, neat paper on the estimating the variance components so that Type I errors aren't less frequent than expected.

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In reply to One follow up question about twin pair means by George Richardson

## If there is a factor that is

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In reply to If there is a factor that is by AdminRobK

## Thanks so much for your

And is it possible in a multivariate ACE model with phenotypes X and Y, to regress Y, which varies only between pairs, on the A and C components for X (which varies within and between)?

Thanks again! - George

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In reply to Thanks so much for your by George Richardson

## Only between is a pairwise variable?

When restricted to a single variable in one of the phenotypes, one has 3 x 3 covariance matrices. This situation eliminates cross-twin cross-variable correlations (they're expected to be the same as within person rP). C is the sole source of variance for the pair measure, so its variance directly estimates C, with A and E for it both being zero. rP directly estimates the C covariance, which is also rC. rA and rE become irrelevant, and may be considered to be zero (or anything else really - they don't feature in the expectations of the model).

It is fine to regress out a pairwise variable prior to analysis - iff the measures are continuous. Regressing variables out of ordinal data up front is not generally appropriate, so I can see an advantage to keeping it in the sort of half-breed univariate/bivariate model :).

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## Re: Only between is a pairwise variable?

I think I'm moving forward with the half breed model. :-)

Is the random effect for between pairs variance, u0j, in the MLM equal to A+C in the ACE model? Seems so.

Thanks you all for helping me achieve cognitive closure on these models!

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In reply to Re: Only between is a pairwise variable? by George Richardson

## Depends on zygosity

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In reply to Depends on zygosity by AdminNeale

## Got it. Yeah that's right.

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