# Fitting genetic models for twin studies

## Contents

In their 2008 paper entitled “Biometrical modeling of twin and family data using standard mixed
model software”,^{(1)} Sophia Rabe-Hesketh and coll. described a mixed-effects model approach to fitting ACE structural equation models to twin data using Stata GLLAMM. This was also discussed in a recent Stata meeting that was held in Germany.

Other papers (not very exhaustive–I have a lot more paper on my HD) dealing with the mixed-effects approach are listed in the bibliography section.

The *de facto* standard software has long been the Mx software developed by Michael Neale, and the Mx scripts Library holds a lot of example datasets and ready-to-run scripts. Now, the Mx software has been ported to R under the OpenMx project. I don’t really like the syntax although it offers two types of model formulation: raw matrices and path specification (as I understand it, the matrix notation was kept for those already familiar with `Mx`

, but maybe some models cannot be expressed using path diagrams).

Some implementations are also available in Mplus^{(2,3)}, SAS^{(4,5)}, or BUGS^{(6)}. I don’t use SAS so I cannot go through extensive review of available code. However, I should mention that I once brought one of their book:
Saxton, A.M. (ed.) 2004. *Genetic Analyses of Complex Traits Using SAS*. Carry, NC: SAS Institute Inc. It has a lot of examples with `PROC MIXED`

.

Stata 12 comes with a module for structural equation modeling (`sem`

), but I hadn’t find enough time to play with it and see how it compares to existing R packages (sem, lavaan or OpenMx). The UCLA server already has some good illusrations of what’s available in the new version, see Problem Solving in Stata 12. But, there are also some good examples of the use of the `sem`

module here: http://sites.google.com/site/ifarwf/home/stata-12-sem-package. About the mixed-effects model approach, there is also an interesting post on Stata blog.

I personally had the opportunity to test OpenMx against Mplus on a small dataset coming from a neuroimaging study:
Wright, I.C., Sham, P., Murray, R.M., Weinberger, D.R., and Bullmore, E.T. (2002). Genetic Contributions to Regional Variability in Human Brain Structure: Methods and Preliminary Results. *NeuroImage*, 17: 256-271.

The article describes an univariate ACE model and a bivariate ACE model (using Cholesky decomposition) on brain and ventricles volumes. The results I got are summarized below.

```
Univariate/Brain
----------------
A C E
Wright 0.66 0.22 0.12
OpenMx 0.753 0.199 0.048
Mx 0.620 0.331 0.048
Mplus 0.753 0.199 0.048
Bivariate/*1=Brain + *2=Ventricle
---------------------------------
A1/A2 C1/C2 E1/E2
Wright 0.67/0.03 0.20/0.46 0.11/0.49 (sum sf + cf)
OpenMx 0.779/0.000 0.176/0.537 0.046/0.463
Mx 0.657/0.021 0.299/0.591 0.045/0.388
```

(Unless I made some mistake, OpenMx and Mx yielded different results, although for univariate ACE model OpenMx and Mplus outputs were identical.)

### References

- Rabe-Hesketh, S., Skrondal, A., and Gjessing, H.K. (2008). Biometrical modeling of twin and family data using standard mixed model software.
*Biometrics*, 64(1): 280-288. - Muthén B., Asparouhov T., and Rebollo I. (2006). Advances in behavioral genetics modeling using Mplus: Applications of factor mixture modeling to twin data.
*Twin Research and Human Genetics*, 9(3): 313-24. - Prescott (2004). Using the Mplus Computer Program to Estimate Models for Continuous and Categorical Data from Twins.
*Behavior Genetics*, 34(1): 17-40. - Zheng, M. (2009). A Biometric Analysis of Twin Data Using PROC MIXED. WUSS Conference.
- Feng, R., Zhou, G., Zhang, M., and Zhang, H. (2009). Analysis of twin data using sas.
*Biometrics*, 65(2): 584–589. - van den Berg, S., Beem, L., and Boomsma, D.I. (2006). Fitting genetic models using Markov Chain Monte Carlo algorithms with BUGS.
*Twin Research and Human Genetics*, 9(3): 334–342. - McArdle, J. and Prescott, C.A. (2005). Mixed-effects variance components models for biometric family analyses.
*Behavior Genetics*, 35(5): 631-652. - McArdle J. (2006). Latent curve analyses of longitudinal twin data using a mixed-effects biometric approach.
*Twin Research and Human Genetics*, 9(3): 343-359. - Ozaki, K. (2008). Twin Analysis on Paired Comparison Data.
*Behavior Genetics*, 38(2): 212-222.