Calculating Cross/Within twin correlations

http://www.ncbi.nlm.nih.gov/pubmed/21646580
and they all mention something like this:
"To estimate MZ and DZ twin correlations within and across
each of the 5 OC symptom dimensions, the data were fitted to a
constrained correlational model in Mx. The MZ and DZ correlations
for each of the symptom subscales (ie, the cross-twin withinsubscale
correlation) provided an indication of the relative contribution
of genetic and environmental factors to the liability of
each dimension (eg, checking)."
I understand this I can't just calculate the regular correlation, since the pairs of twins are inter-changeable within them, so this is more like an intra-class correlation.
I've been checking a lot of openMX documentation, but I can't find how to exactly do it. I understand I need to add constrains to the model, but I don't know how.
Any example or guiding light will be very appreciated.
Afterwards I'll try to fit an ACE model to the data. The univariate example found in the openMX documentation is very clear so I hope I won't have trouble, but I might have more trouble when I try a bivariate one.
Thanks a lot in advance!
Equate means & variances T1=T2
There's an ordinal data example here.
http://www.vipbg.vcu.edu/NIDAworkshop2012/twinMulAceOrd.R
and I think a continuous one here
http://www.vipbg.vcu.edu/tc2012/tc2012_OpenMx.shtml
Log in or register to post comments
In reply to Equate means & variances T1=T2 by neale
Thank you very much for your
I'm providing the resulting code, that first fits a saturated bivariate model (with the mentioned restrictions for twins), then a Cholesky ACE, then an Independent Pathway ACE, and finally a Common Pathway ACE. One thing I noticed is that in the bivariate case, the Cholesky ACE actually has fewer parameters (11) than the rest (18, 14, 13, respectively).
So I understand the correlations I desired in the fist place can be calculated from the covariance matrix provided here:
expectedMeansCovariances(bivTwinSatFit)
About the rest of the models, in the bivariate case, which one is the most commonly used? I find it easier to interpret the Common Pathway one, but the Cholesky has fewer parameters. I just find difficult to interpret the path coefficients that are shared among the 2 variables. Is there any other alternative?
Thanks again for all your help! Cheers!
Log in or register to post comments
In reply to Thank you very much for your by DanielC
More parameters than saturated model = bad thing
It does have a constraint on the latent variance, so we use 2 parameters up there. If the two loadings are free, that's another 2, then there are 3 each for the residual variance components. This adds up to 10. However, there are only 6 'distinct' statistics in the Covariance matrix of MZ's and only the cross-twin statistics differ in the DZ's (the symmetric 2x2 block), which gives another 3, making a total of 9. So I have a hard time seeing how the common pathway model would be identified in the bivariate case without a constraint such as fixing the factor loadings to be equal, which may limit the interpretability.
Possibly, you are looking for a way to interpret the Cholesky estimates? Most important is to calculate the product with the transpose (say lower matrix, a, of path coefficients generates matrix A with the algebra a%*%t(a) and same for C & E) Each variance component type, can be "standardized" by dividing by the sum A+C+E (the phenotypic covariance). Then you would have proportions of variance on the diagonal, and contributions to the covariance on the off diagonal (since A, C and E off -diagonals can be of different sign, the off-diagonal elements of (A/(A+C+E) are not strictly proportions). Also possible is to use cov2cor on the A matrix to inspect the genetic correlation.
Log in or register to post comments