# Another Means Model question

I have a couple of queries relating to means modelling but more on the conceptual side rather than OpenMx scripting.

1. This is just a general question. To test means models for eye traits ideally requires an assessment of Right vs Left measures, in addition to twin order and then zygosity. Most of the ophthalmic heritability papers I've read are haphazard in how they approach the R vs L issue. Some use one eye as the representative phenotype, others the mean of R and L, and some a Cholesky of both. If you test R and L means and find this constrained model is an acceptable fit compared to the saturated model, does that effectively mean there is nothing to be gained from using information from both eyes in a multivariate (cholesky) analysis? ie could you just take the mean of R and L eyes and obtain a similar result?

I'm not sure how much laterality is an issue with other twin researchers?

2. The variables in my dataset are principal components of quantitative measures of optic nerve head shape. I want to use the PC scores as input variables in heritability analyses. I've found a strange problem when looking at the means of these PC scores (e.g. the first 6 PCs):

model:LEFT, means:expMeanLEFT

L_PC1 L_PC2 L_PC3 L_PC4 L_PC5 L_PC6

[1,] -0.002266072 -0.0002236406 0.001309996 -0.0003326820 0.0006076135 0.001867347

model:RIGHT, means:expMeanRIGHT

R_PC1 R_PC2 R_PC3 R_PC4 R_PC5 R_PC6

[1,] 0.002266055 0.0002236404 -0.001309996 0.0003326712 -0.0006076171 -0.001867343

When I try to run this, I get a red status. From what I can understand, because a PCA mean centres your data at zero, if you take two roughly equal sample sizes for a PC, the means will be opposite in sign, so that the grand mean is zero. The same also happens when I compare the means for twin 1 vs twin 2. Can you not fit a means model in this case? (sorry, if I've not explained it clearly).

Any thoughts/tips would be appreciated. Thanks in advance.

Paul Sanfilippo

## "If you test R and L means

No. Having equal means does not mean perfect covariance between eyes. Taking the mean of both eyes essentially down-weights the eye-specific variance components. It can cause the problems known to occur with sum-scores (see Neale, M.C., Lubke G., Aggen S.H. & Dolan, C.V. (2005) Problems with using sum scores for estimating variance components: contamination and measurement noninvariance. Twin Research and Human Genetics 8:553-68. at http://www.vipbg.vcu.edu/vipbg/neale-articles.shtml#NEALE05).

It seems reasonable that the means have ended up distributed in this way. What is critical is that twin 1 and twin 2 variables, and MZ and DZ, are not standardized separately. The standardization should be conducted on the entire sample, which allows the four observed means (T1, T2, MZ & DZ) to differ.

The pattern of means for right and left eyes is only an issue for multivariate analysis. Testing for mean differences between eyes may still be meaningful here. For example, if there are average shape differences then the means should be further away from zero. Looking at the data it doesn't look like there are such differences, but without std errors it's not possible to tell.

Log in or register to post comments

In reply to "If you test R and L means by neale

## Thanks for the help Mike.

Regards,

Paul

Log in or register to post comments