I have a single common factor and several manifest phenotypic variables. I'd like to determine the relationship between the factor and several SNPs of interest.

I'm not sure exactly how to model the factor means with respect to SNP status (coded 0,1,2 for homozygotes, heterozygotes, and the other homozygotes). A preliminary thought was to fit a multi-group CFA with one group for each genotype, and allow the means to vary across groups. There must be a better way than this that involves a single-group CFA means model.

I've seen plenty scripts that model the manifest variable means, but nothing where the factor means were modeled.

Any thoughts, references, or example scripts? By the way, I've posted here in the past and am very impressed and appreciative of the rapid and helpful responses!

-Scott

Yes, multiple groups would work, but it can be a nuisance when the number of loci or alleles increases. I would use a definition variable or two to specify the predicted factor means. One place to look for a thorough classic Mx approach is Posthuma D, de Geus EJ, Boomsma DI, Neale M.C.: Combined linkage and association tests in mx. Behavior Genetics 2004; 34:179-196 (http://www.vipbg.vcu.edu/vipbg/Articles/behavgen-combined-2004.pdf). The general approach taken here was to build up a matrix of the predicted means for allele1 (rows) and allele2 (columns), which allows for additive effects for each allele. So if the mean deviations for A and a are in a 1x2 vector P and which can be kronecker multiplied by a 2x1 unit matrix U. Then P %x% U + t(P %x% U) gives a matrix of additive effects. Dominance effects are only found on the off-diagonal and can be set up with a subdiagonal matrix and its transpose.

There exist classic Mx scripts for this purpose, and even perl helper functions to build classic Mx scripts, as described in Medland & Neale An integrated phenomic approach to multivariate allelic association Eur J Hum Genet. 2010 Feb;18(2):233-9. Epub 2009 Aug 26 (see http://www.vipbg.vcu.edu/~sarahme/WriteMx/index.html). This paper describes modeling allelic effects which can be either at the factor level or at the individual measure (residual-specific) level.

Anyway, somewhat complex topic but I hope this helps.

Thanks so much for the references, they're very helpful. It seems the scripts referenced are only applicable to DZ twins or sib pairs (optionally with parental info). My sample is about half MZ twins as well, and I can't determine how to incorporate MZ information into those models. I don't want to just drop the MZs, and there must be a clever way to use their genetic and/or phenotypic information to inform estimation of an association effect.

Actually, after a little more searching, I think I may have found some example scripts that could suit my needs. They're at http://www.psy.vu.nl/mxbib/index.php?page=mx_tree&tree_list=1,2,3,20,47,69&last=69.

The only issue now is incorporating these univariate tests for association and linkage into a relatively complex (for me) bifactor common pathway model with means models on the common and group factors.

-Scott

Right, the case for MZ's is really pretty simple (there's no linkage information). Assuming complete pairwise genetic marker data, the same model for the means of the DZ's can be used - the alleles will populate appropriately, even if the MZ's are perfectly correlated in this respect. The only difference is in the model for their covariance, but this is usually simple to convert from the DZ case - just a matter of getting rid of the .5's (and .25's if there are any) in the predicted covariance matrix.