R/gmcmtxZ.R

In generalCorr: Generalized Correlations, Causal Paths and Portfolio Selection

#' compute the matrix R* of generalized correlation coefficients.
#' 
#' This function checks for missing data separately for each pair using
#' \code{kern} function to kernel regress x on y, and conversely y on x. It
#'  needs the library `np' which reports R-squares of each regression. This function
#' reports their square roots with the sign of the Pearson correlation coefficients.
#' Its appeal is that it is asymmetric yielding causal direction information.
#' It avoids the assumption of linearity implicit in the usual correlation 
#' coefficients.
#' 
#' @param mym {A matrix of data on variables in columns}
#' @param nam {Column names of the variables in the data matrix}
#' @return  A non-symmetric R* matrix of generalized correlation coefficients
#' @importFrom stats cor
#' @importFrom stats complete.cases
#' @note This allows the user to change \code{gmcmtx0} and further experiment with my code.
#' @author Prof. H. D. Vinod, Economics Dept., Fordham University, NY
## @seealso %% ~~objects to See Also as \code{\link{help}}, ~~~
#' @references Vinod, H. D. `Generalized Correlation and Kernel Causality with 
#'  Applications in Development Economics' in Communications in 
#'  Statistics -Simulation and Computation, 2015, 
#'  \doi{10.1080/03610918.2015.1122048} 
#' @concept  kernel regression
#' @concept R* asymmetric correlations
#' @examples
#' 
#' \dontrun{
#' set.seed(34);x=matrix(sample(1:600)[1:99],ncol=3)
#' colnames(x)=c('V1', 'v2', 'V3')
#' gmcmtxZ(x)
#' }
#' 
#' @export

gmcmtxZ <- function(mym, nam = colnames(mym)) {
    # mym is a data matrix with n rows and p columns some NAs may be present in the
    # matrix
    p = NCOL(mym)
    # print(c('p=',p))
    out1 = matrix(1, p, p)  # out1 stores asymmetric correlations
    for (i in 1:p) {
        x = mym[, i]
        ava.x = which(!is.na(x))
        for (j in 1:p) {
            if (j > i) 
                {
                  y = mym[, j]
                  ava.y = which(!is.na(y))  #ava means non-missing
                  ava.both = intersect(ava.x, ava.y)
                  newx = x[ava.both]
                  newy = y[ava.both]
                  c1 = cor(newx, newy)
                  sig = sign(c1)
                  mod.1 = kern(dep.y = x, reg.x = y)
                  mod.2 = kern(dep.y = y, reg.x = x)
                  corxy = sqrt(mod.1$R2) * sig
                  coryx = sqrt(mod.2$R2) * sig
                  out1[i, j] = corxy
                  out1[j, i] = coryx
                }  #endif
        }  #end j loop
    }  #end i loop
    colnames(out1) = nam
    rownames(out1) = nam
    return(out1)
}