Hello,
I was reading the book by Neale and Maes (2004) and they have a nice part about how to check the identification of a univariate twin model using matrix algebra (p. 104).
It is possible to check the identification of the model by representing the expected (co-)variances as a system of equation in matrix algebra:
Ax=b
where x is the vector of parameters, b is the vector of observed statistics and A is the matrix containing the weights of elements in x.
In the univariate case (ACE model), x=(a^2,c^2,e^2).
My first question is: Is it possible to express x=(a,c,e) instead of x=(a^2,c^2,e^2)= How would Ax=b look like in this case?
My second question is: How would like the Ax=b system of equation for a bivariate Cholesky model? Here my parameters would be x=(a11,a21,a22,c11,c21,c22,e11,e21,e22). However, as some of the covariances are a function of the squared parameters, I don't know how to construct A in this case.
I hope you understand the point of my questions.
Thank you,
Benny
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This paper goes into a lot of detail about how single-phenotype twin and family models can be identified.
Hunter, M.D., Garrison, S.M., Burt, S.A. et al. The Analytic Identification of Variance Component Models Common to Behavior Genetics. Behav Genet 51, 425–437 (2021). https://doi.org/10.1007/s10519-021-10055-x
Also, the
mxCheckIdentification()function takes a more general approach by checking the dimension (i.e., rank) of the mapping from the free parameters to the summary statistics. See its help page for more details.Finally, for multi-phenotype models the same process of identification applies. It's just a little more complicated. Once you read the paper and check out the function, it should seem straightforward.