# Sex-limitation, bivariate and other-sex twins questions

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Joined: 10/10/2018 - 17:20
Sex-limitation, bivariate and other-sex twins questions

Hi everyone,

I want to test a bivariate model of two phenotypes. As I am very new to all this (and unfortunately not from the US and so can't attend the workshops) I researched the internet and ended up succeeding in running a bivariate model script and learning a bit about it (the script I took is from http://ibg.colorado.edu/cdrom2016/maes/UnivariateAnalysis/two/twoACEc.R).
However, I thought it would be wise to make sure there are no various sex-differences in my model. After reading a few threads in the forum I understood there are substantial problems in running a multivariate sex-limitation model. So several question:

1. 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? If not, what are other options I have?

2. 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).

3. 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?

4. 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)?

Thank you so very much!

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Joined: 01/24/2014 - 12:15
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.

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Joined: 10/10/2018 - 17:20
Follow-up questions

First of all - Thank you very much for your detailed reply!

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.

This sounds great. Do you think there will be a possibility to get/publish either of these syntaxes? I've seen before the Neale et al., (2006) paper on the subject, but as a beginner at complex ACE models and OpenMx their solutions for implementing multivariate-sex-limitaion models seemed to complex for me to implement on my own, unfortunately.

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?

There are some evidence for mean differences in these phenotypes in the literature. To add on that, I just realised I interpreted the results of mxCompare wrong, and for one of the phenotypes the best fitting model is of quantitative sex-limitaion. These leads me back to the first point of how great it will be to receive such a syntax, because for now I don't have a solution.

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

I am using DZO for the univariate sex-limitation models, but not in the bivariate models without sex-limitation. I was wondering if the no sex-limitation models were the best fit for the data and I go back to the bivariate model, is there a need or a way to add the DZO to the no sex-limitation bivariate model. It is less relevant now as there is a quantitative sex-difference in one of the phenotypes. However, I think I'm not clear on something regarding this issue. The results of a sex-limitation test are with different estimates for males and females, and this is true for the no sex-limitation model as well. So, a. just to make sure - those estimates are based on the DZO data as well? b. if there was no sex-limitation, should I have taken the results of the no sex-limitation model from within the context of the sex-limitation test or to go back to a "regular" univariate model? c. If I should stay with no sex-limitation model from within the sex-limitation model, what is the best way to combine the results of males and females? d. If I should go back to the "regular" univariate model, should I incorporate DZO and how (this was my original question).

Everything else was clear, and everything was very helpful - thank you so very much!

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Joined: 01/24/2014 - 12:15

I just noticed I never addressed this:

So, a. just to make sure - those estimates are based on the DZO data as well? b. if there was no sex-limitation, should I have taken the results of the no sex-limitation model from within the context of the sex-limitation test or to go back to a "regular" univariate model? c. If I should stay with no sex-limitation model from within the sex-limitation model, what is the best way to combine the results of males and females? d. If I should go back to the "regular" univariate model, should I incorporate DZO and how (this was my original question).

But I'm afraid I'm confused and don't really follow the question...?

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Joined: 10/10/2018 - 17:20
Thank you for the reply.

Thank you for the reply.

First, I wanted to know if there are any news regarding the bivariate sex-limitation model syntax? I think I have no way to advance without it.

Second, regarding my questions, I was trying to understand better how to interpret even univariate sex-limitation results, and I had a few questions about it, that I'll try to write clearer:
a. When estimating a sex-limitation model, one of the models we test is a model without sex-limitation, for which the estimates are separate for males and females. I wanted to make sure that these estimates are based on the DZO data as well. b. If I find in a univariate sex-limitation tests that the best model is a model without sex-limitation, should I take the estimates from the no sex-limitation model within the sex-limitation tests, to go back to the estimates from the "regular" univariate model (the one for which I didn't tested sex-limitation). c. If the answer to "b" is that I should use the estimates from the no sex-limitation model but that is within the sex-limitation tests, the estimates are separate for males and females. But in this scenario, there is no sex-limitation, so the gender separation is meaningless and I'm not sure how to combine the estimates for males and females. d. If the answer to "b" is that in a scenario of no sex-limitation, I should go back to the "regular" univariate model (that didn't consider sex-limitation in any way), this model uses data only from MZ and DZS. If I find there is no sex-limitation, I'm wondering if I should base my estimates of the univariate model on data of DZO as well, and than how should it be added to a "regular" univariate model?

I hope it was clearer now, thank you so much!

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Joined: 03/01/2013 - 14:09
Hi Noam

Hi Noam

Your questions suggest some confusion. I attempt to answer them and clarify here:
a. When estimating a sex-limitation model, one of the models we test is a model without sex-limitation, for which the estimates are separate for males and females. I wanted to make sure that these estimates are based on the DZO data as well.

Sex-limitation is when factors operate differently in males vs. females. When you say "a model without sex-limitation, for which the estimates are separate for males and females" it is self-contradictory, because if males and females have different parameter estimates for a c and e, then it is a model with sex-limitation. Supposing that you mean that both males and females are in the model, but parameters have been equated between males and females (so they are not "separately" estimated) then yes indeed they are making use of data from all five zygosity-sex groups.

b. If I find in a univariate sex-limitation tests that the best model is a model without sex-limitation, should I take the estimates from the no sex-limitation model within the sex-limitation tests, to go back to the estimates from the "regular" univariate model (the one for which I didn't tested sex-limitation).

If there's no sex-limitation at all (neither means/thresholds nor variance components differ by sex) then the results should be exactly the same from a 5-group model and a 2-group model.

c. If the answer to "b" is that I should use the estimates from the no sex-limitation model but that is within the sex-limitation tests, the estimates are separate for males and females. But in this scenario, there is no sex-limitation, so the gender separation is meaningless and I'm not sure how to combine the estimates for males and females.

There should NOT be different estimates for males and females in this scenario. If there are differences, the estimates for males and females have not been equated when they should have been. Usually it's just a matter of making the matrices have the same parameter labels in both groups.

If the answer to "b" is that in a scenario of no sex-limitation, I should go back to the "regular" univariate model (that didn't consider sex-limitation in any way), this model uses data only from MZ and DZS. If I find there is no sex-limitation, I'm wondering if I should base my estimates of the univariate model on data of DZO as well, and than how should it be added to a "regular" univariate model?

Yes, the DZOS pairs should be included in the two-group analysis (being more DZ pairs). Then the results should agree between the 5-group and the 2-group models. The same number of parameters, the same estimates and standard errors should emerge.

HTH
Cheers
Mike

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Joined: 10/10/2018 - 17:20
Thank you very much for your

Thank you very much for your detailed answers, they were a great help in clearing up the confusions I still had and drew a very clear picture.
Now I just need to find a bivariate sex-limitation model :)

Thank you!