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