#' @title Compute all regression coefficients from a covariance matrix
#'
#' @description Compute all direct regression coefficients (direct effects), \code{B} from a covariance matrix starting from the first variable to the last (order matter).
#' @param S A covariance matrix.
#'
#' @return A lower triangular matrix containing all direct effects (regression coefficients)
#' @export
#'
#' @examples
#' S <- matrix(c( 1, .2, .4,
#' .2, 1, .3,
#' .4, .5, 1), ncol = 3, nrow = 3)
#' cov2beta(S)
cov2beta = function(S){
p = dim(S)[1] # Nombre de variable
BETA = matrix(0, p, p,
dimnames = list(rownames(S),
colnames(S))) # Matrice vide
# Boucle de calcul pour la covariance de la variable i (i = 1:(p-1))
for(i in 1:(p-1)){
BETA[i+1, 1:i] = solve(S[1:i, 1:i], S[1+i, 1:i])
}
return(BETA)
}
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