isqrtfa: Inverse square-root of a matrix based on its factor...
In ERP: Significance Analysis of Event-Related Potentials Data

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

emfa, ifa

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