Sex-limitation, bivariate and other-sex twins questions

After reading a few threads in the forum I understood there are substantial problems in running a multivariate sex-limitation model.

I do not believe a generic reference script (such as those used at Boulder) for polyphenotype sex-limitation existed until recently; indeed, I wrote a custom polyphenotype-sex-limitation script for for a collaborator a few months ago. However, a few weeks ago, Hermine Maes told me she had written a generic reference script, but I haven't seen it, and have not been able to get in touch with her in the 6 days since you started this thread.

If the sex differences are not my focus but rather I just want to make sure it doesn't need to be included in the model, is it possible to run 2 separate univariate sex-limitation models? When doing that, I found in one trait the no sex-limitation model is significantly better than the sex-limitation non-scalar models, and in the other trait I found that there are no significant differences between the different sex-limitation models, but than the no sex-limitation is the most parsimonious and can be chosen. Is it ok to do that and than run my regular bivariate model with no sex-limitation?

Probably, but I guess sex-limitation could still be revealed in a diphenotype analysis, in the correlations between the two traits (and particularly the genetic correlations among the DZO twins). If I were a journal referee, I would probably criticize a manuscript that neglected to carry out the diphenotype analysis. Is there any evidence for sex-limitation in your phenotypes in the existing literature?

In the univariate sex-limitation syntax I found (https://ibg.colorado.edu/cdrom2018/deleeuw/sexLimitation/) there is no model for the scalar sex-limitation model. This was also the case for a different syntax I found. Is there a reason this is not tested? If it needs to be tested, do you have recommendation for where to find this syntax (I used the Boulder 2018 workshop one).

No, there is a scalar sex-limitation model in that script, modelACEq. The comment on line 167 of that script is wrong, and portions of that script have likely been copy-pasted to elsewhere with the error preserved. In modelACEq, parameter 'ra11' is being fixed to 1, and therefore, opposite-sex DZ twins will share an expected 0.5 of alleles at trait-relevant loci, but the model still allows for sex differences in the biometrical decomposition into A, C, and E. That makes the model a scalar or "quantitative" sex-limitation model.

If the answer to the first question is yes, and there seem to be no sex differences between sexes, I think I can than insert DZ other-sex twins into my no sex-limitation bivariate ACE model and increase the power of my model, is it correct? If so, what is the correct way to include DZ-O twins in the model?

Do you mean you aren't using your DZO twins already in your monophenotype sex-limitation models?

Last, as I mentioned, I found the bivariate syntax online. From the presentation attached to the syntax, I think the syntax is for a bivariate Cholesky model. How can I make sure from the script this is actually the case and it is not a different model (e.g., common factors)?

This,

# Create Matrices for Path Coefficients
pathA     <- mxMatrix( type="Lower", nrow=nv, ncol=nv, free=TRUE, values=svPaD, label=labLower("a",nv), lbound=lbPaD, name="a" ) 
pathC     <- mxMatrix( type="Lower", nrow=nv, ncol=nv, free=TRUE, values=svPaD, label=labLower("c",nv), lbound=lbPaD, name="c" )
pathE     <- mxMatrix( type="Lower", nrow=nv, ncol=nv, free=TRUE, values=svPeD, label=labLower("e",nv), lbound=lbPaD, name="e" )
 
# Create Algebra for Variance Comptwonts
covA      <- mxAlgebra( expression=a %*% t(a), name="A" )
covC      <- mxAlgebra( expression=c %*% t(c), name="C" ) 
covE      <- mxAlgebra( expression=e %*% t(e), name="E" )
 
# Create Algebra for expected Variance/Covariance Matrices in MZ & DZ twins
covP      <- mxAlgebra( expression= A+C+E, name="V" )

, is a dead giveaway. The biometric covariance matrices ('A', 'C', and 'E' in this case) are each being parameterized in terms of a lower-triangular matrix times its transpose, and the phenotypic covariance matrix is merely the sum of the biometric covariance matrices.

BTW, on the matter of polyphenotype sex-limitation, Neale, Røysamb, & Jacobson (2006) may be a useful reference for you.