Assuming you’re using “C” to denote Covariance (“Cov” is more common), that seems right.
It’s typical that the noise covariance is diagonal, since a general covariance matrix for the noise would render use of a latent variable unnecessary (the whole covariance matrix for x could be explained by the covariance matrix of the “noise”, which would actually include the signal as well). (Though it could be that some people use a non-diagonal covariance matrix that is subject to some other sort of constraint that makes the procedure meaningful.)
Of course, it is very typical for people to use factor analysis models with more than one latent variable. There’s no a priori reason why “intelligence” couldn’t have a two-dimensional latent variable. In any real problem, we of course don’t expect any model that doesn’t produce a fully general covariance matrix to be exactly correct, but it’s scientifically interesting if a restricted model (eg, just one latent variable) is close to being correct, since that points to possible underlying mechanisms.
Assuming you’re using “C” to denote Covariance (“Cov” is more common), that seems right.
It’s typical that the noise covariance is diagonal, since a general covariance matrix for the noise would render use of a latent variable unnecessary (the whole covariance matrix for x could be explained by the covariance matrix of the “noise”, which would actually include the signal as well). (Though it could be that some people use a non-diagonal covariance matrix that is subject to some other sort of constraint that makes the procedure meaningful.)
Of course, it is very typical for people to use factor analysis models with more than one latent variable. There’s no a priori reason why “intelligence” couldn’t have a two-dimensional latent variable. In any real problem, we of course don’t expect any model that doesn’t produce a fully general covariance matrix to be exactly correct, but it’s scientifically interesting if a restricted model (eg, just one latent variable) is close to being correct, since that points to possible underlying mechanisms.