R/rstar.R

In generalCorr: Generalized Correlations, Causal Paths and Portfolio Selection

#' Function to compute generalized correlation coefficients r*(x,y).
#'
#' Uses Vinod (2015) definition of generalized (asymmetric) correlation
#' coefficients.  It requires kernel regression of x on y obtained by using the `np' package.
#' It also reports usual Pearson correlation coefficient r and p-value for testing
#' the null hypothesis that (population r)=0.
#' @param x {Vector of data on the dependent variable}
#' @param y {Vector of data on the regressor}
#' @importFrom stats cor.test
#' @return Four objects created by this function are:
#' \item{corxy}{r*x|y or regressing x on y}
#' \item{coryx}{r*y|x or regressing y on x}
#' \item{pearson.r}{Pearson's product moment correlation coefficient}
#' \item{pv}{The p-value for testing the Pearson r}
#' @note This function needs the kern function which in turn needs the np package.
#' @author Prof. H. D. Vinod, Economics Dept., Fordham University, NY
#' @seealso See Also \code{\link{gmcmtx0}} and  \code{\link{gmcmtxBlk}}.
#' @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}
#'
#' @references Vinod, H. D. 'Matrix Algebra Topics in Statistics and Economics
#' Using R', Chapter 4 in Handbook of Statistics: Computational Statistics
#' with R, Vol.32, co-editors: M. B. Rao and C.R. Rao. New York:
#' North Holland, Elsevier Science Publishers, 2014, pp. 143-176.
#' @concept asymmetric  p-values
#' @examples
#' x=sample(1:30);y=sample(1:30); rstar(x,y)
#'
#' @export

rstar <- function(x, y) {
    c1 = cor.test(x, y)
    sig = sign(c1$estimate)
    pv = c1$p.value
    pearson.r = c1$estimate
    mod.1 = kern(dep.y = x, reg.x = y)
    mod.2 = kern(dep.y = y, reg.x = x)
    corxy = sqrt(mod.1$R2) * sig
    coryx = sqrt(mod.2$R2) * sig
    list(corxy = corxy, coryx = coryx, pearson.r = pearson.r, pv = pv)
}