R/eff_dof.R

In varycoef: Modeling Spatially Varying Coefficients

tr <- function(A) {
  # computes the trace of a matrix
  sum(diag(A))
}


eff_dof <- function(cov.par, X, cov_func, outer.W, taper) {

  n <- nrow(X)
  p <- length(outer.W)
  nug.var <- cov.par[length(cov.par)]
  Sigma <- Sigma_y(cov.par, cov_func, outer.W, taper)

  iSigma <- solve(Sigma)

  XtiS <- crossprod(X, iSigma)

  # trace of hat matrix (equation 15 in Mueller et al. 2013, Stat. Sci.)
  as.numeric(nug.var * tr(solve(XtiS %*% X) %*% XtiS %*% iSigma %*% X) +
    n - nug.var * tr(iSigma))
}

tr_Sigma <- function(cov.par, X, cov_func, outer.W, taper) {

  n <- nrow(X)
  nug.var <- tail(cov.par, 1)
  p <- length(outer.W)


  tr(Sigma_y(cov.par, cov_func, outer.W, taper)) - nug.var*n
}