Description Usage Arguments Details Value Author(s) References See Also Examples
This function is not supposed to be called directly by users. It is needed in functions erpfatest
and erpFtest
implementing factor-adjusted testing methods.
1 | isqrtfa(Psi, B)
|
Psi |
m-vector of specific variances, where m is the number of rows and columns of the matrix. |
B |
mxq matrix of loadings, where q is the number of factors |
If Sigma has the q-factor decomposition Sigma=diag(Psi)+BB', then the function returns a matrix Omega such that Sigma^-1 = Omega Omega'. Equivalently, Omega' Sigma Omega = I.
The mxm matrix Omega (see the details Section).
David Causeur, IRMAR, UMR 6625 CNRS, Agrocampus Ouest, Rennes, France.
Woodbury, M.A. (1949) The Stability of Out-Input Matrices. Chicago, Ill., 5 pp
1 2 3 4 5 6 7 | data(impulsivity)
erpdta = as.matrix(impulsivity[,5:505]) # erpdta contains the whole set of ERP curves
fa = emfa(erpdta,nbf=20) # 20-factor modelling of the ERP curves in erpdta
Sfa = diag(fa$Psi)+tcrossprod(fa$B) # Factorial estimation of the variance
iSfa = ifa(fa$Psi,fa$B)$iS # Matrix inversion
isqrtSfa = isqrtfa(fa$Psi,fa$B) # Inverse square-root of Sfa
max(abs(tcrossprod(isqrtSfa)-iSfa)) # Checks that isqrtSfa x t(isqrtSfa) = iSfa
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