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
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 (
OpenMx). The UCLA server already has some good illusrtations 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 neuro-imaging 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 univariate and bivariate ACE models, fitted 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.)