Is there a way to get the fisher information matrix and\or the asymptotic covariance matrix of the parameter estimates as defined by Jöreskog 1973 (Appendix 2) out of MPlus. i.e. the matrix from which the diagonals give the standard errors of the parameter estimates.
The reason I ask is that I am trying to learn what goes on behind the scene's in SEM. I thus used the tutorial by J.Miles in MBR and Kaplan to write my own CFA functions in R. Long story short all the estimates, fit, etc. are the same as the MPlus output for the same model but not my standard errors.
The optim function for ML estimation in R produces a hessian matrix which I then inverted. Once this is inverted I should be able to take the square root of the diagonials to get the SEs of the estimates. While I do get SEs that are proportional to MPlus my vcov of parameter estimates needs to be multipled by a constant (in my case .0056) to get the same SE estimates as MPlus.
Would anyone know where this constant comes from and how I determin its value?
It is certainly to do with n but my exploration (varying sample sizes and number of items) is that the constant is 2/n rather than n/(n-1). This is fine as I can now use this constant BUT I dont really like that I dont know where it comes from.
I think (think) that it is the expected fisher information matrix rather than the observed but to be honest I am working at my limits here.