getF.Sigma | R Documentation |
Computes the minimum of the chosen fitting-function given the model-implied and the observed (or population) covariance matrix.
The ML fitting function is:
F_min = tr(S %*% SigmaHat^-1) - p + ln(det(SigmaHat)) - ln(det(S))
. When a meanstructure is included,
(mu - muHat)' SigmaHat^-1 (mu - muHat)
is added.
The WLS fitting function is:
F_min = (Sij - SijHat)' V (Sij - SijHat)
where V is the inverse of N times the asymptotic covariance matrix of the sample statistics (Gamma; N x ACOV(mu, vech(S))).
For DWLS, V is the diagonal of the inverse of diag(NACOV), i.e. diag(solve(diag(Gamma))).
For ULS, V = I. ULS has an unknown asymptotic distribution, so it is actually irrelevant, but provided for the sake of completeness.
getF.Sigma(SigmaHat, S, muHat = NULL, mu = NULL, fittingFunction = "ML")
SigmaHat |
model implied covariance matrix |
S |
observed (or population) covariance matrix |
muHat |
model implied mean vector |
mu |
observed (or population) mean vector |
fittingFunction |
one of |
Returns Fmin
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