mrdisp: Multiple Rankings (MR) dispersion function.
In kloke/mrfit: Multiple rankings estimates

Description Usage Arguments Details Value Author(s) References See Also Examples

A seperate ranking (and dispersion function) is formed for each of the centers/blocks/clusters. The MR dispersion function is the sum of these separate dispersion functions. The objective function for the MR estimator is the minimizor of this MR dispersion function.

1	mrdisp(x, y, center, beta)

`x`	n by p design matrix
`y`	n by 1 response vector
`center`	n by 1 vector denoting block (cluster) membership
`beta`	p by 1 vector

The multiple rankings (MR) dispersion function is defined as D(beta) = sum Dj(beta) where Dj(beta) is Jaeckel's (1972) dispersion function for the jth cluster/center/block. A separate set of rankings is computed for each center. D(beta) is the objective function to minimize for the MR estimate of beta.

Returns the MR dispersion function evaluated at beta.

John Kloke kloke@biostat.wisc.edu

Jaeckel, L. A. (1972). Estimating regression coefficients by minimizing the dispersion of residuals. Annals of Mathematical Statistics, 43, 1449 - 1458.

Rashid, M.M., McKean, J.W., Kloke, J.D. (2011). R Estimates and Associated Inferences for Mixed Models with Covariates in a Multi-Center Clinical Trial. Statistics in Biopharmaceutical Research.

mrfit

### Internal function ###
## The function is currently defined as
function (x, y, center, beta) 
{
    a <- unique(center)
    nc <- length(a)
    Dvec <- rep(0, nc)
    for (j in 1:nc) {
        x1 <- as.matrix(x[center == a[j], ])
        y1 <- y[center == a[j]]
        nj <- length(y1)
        e <- y1 - x1 %*% beta
        sj <- as.matrix(sqrt(12) * (rank(e, ties.method = "random")/(nj + 
            1) - 0.5))
        Dvec[j] <- t(sj) %*% e
    }
    sum(Dvec)
  }