Nothing
##########################################################
####### el.test(), from Owen, Modified by Mai Zhou #######
##########################################################
el.test <- function( x, mu, lam, maxit=25, gradtol=1e-7,
svdtol = 1e-9, itertrace=FALSE ){
x <- as.matrix(x)
n <- nrow(x)
p <- ncol(x)
mu <- as.vector(mu)
if( length(mu) !=p )
stop("mu must have same dimension as observation vectors.")
if( n <= p )
stop("Need more observations than length(mu) in el.test().")
z <- t( t(x) -mu )
#
# Scale the problem, by a measure of the size of a
# typical observation. Add a tiny quantity to protect
# against dividing by zero in scaling. Since z*lam is
# dimensionless, lam must be scaled inversely to z.
#
TINY <- sqrt( .Machine$double.xmin )
scale <- mean( abs(z) ) + TINY
z <- z/scale
if( !missing(lam) ){
lam <- as.vector(lam)
lam <- lam*scale
if( logelr(z,rep(0,p),lam)>0 )lam <- rep(0,p)
}
if( missing(lam) )
lam <- rep(0,p)
#
# Take some precaution against users specifying
# tolerances too small.
#
if( svdtol < TINY )svdtol <- TINY
if( gradtol < TINY)gradtol <- TINY
#
# Preset the weights for combining Newton and gradient
# steps at each of 16 inner iterations, starting with
# the Newton step and progressing towards shorter vectors
# in the gradient direction. Most commonly only the Newton
# step is actually taken, though occasional step reductions
# do occur.
#
nwts <- c( 3^-c(0:3), rep(0,12) )
gwts <- 2^( -c(0:(length(nwts)-1)))
gwts <- (gwts^2 - nwts^2)^.5
gwts[12:16] <- gwts[12:16] * 10^-c(1:5)
#
# Iterate, finding the Newton and gradient steps, and
# choosing a step that reduces the objective if possible.
#
nits <- 0
gsize <- gradtol + 1
while( nits<maxit && gsize > gradtol ){
arg <- 1 + z %*% lam
wts1 <- as.vector( llogp(arg, 1/n) )
wts2 <- as.vector( -llogpp(arg, 1/n) )^.5
grad <- as.matrix( -z*wts1 )
#############grad <- as.vector( apply( grad, 2, sum ) )
grad <- as.vector(rowsum(grad, rep(1, nrow(grad)) ) )
gsize <- mean( abs(grad) )
hess <- z*wts2
# -1
# The Newton step is -(hess'hess) grad,
# where the matrix hess is a sqrt of the Hessian.
# Use svd on hess to get a stable solution.
#
## may try La.svd() in R (v. > 1.0) for better LAPACK.
## or use QR decomposition on hess to solve it.
svdh <- svd( hess )
## svdh <- La.svd( hess )
if( min(svdh$d) < max(svdh$d)*svdtol )
svdh$d <- svdh$d + max(svdh$d)*svdtol
nstep <- svdh$v %*% (t(svdh$u)/svdh$d)
## nstep <- t(svdh$vt) %*% (t(svdh$u)/svdh$d)
nstep <- as.vector( nstep %*% matrix(wts1/wts2,n,1) )
gstep <- -grad
if( sum(nstep^2) < sum(gstep^2) )
gstep <- gstep*(sum(nstep^2)^.5/sum(gstep^2)^.5)
ologelr <- -sum( llog(arg,1/n) )
ninner <- 0
for( i in 1:length(nwts) ){
nlogelr <- logelr( z,rep(0,p),lam+nwts[i]*nstep+gwts[i]*gstep )
if( nlogelr < ologelr ){
lam <- lam+nwts[i]*nstep+gwts[i]*gstep
ninner <- i
break
}
}
nits <- nits+1
if( ninner==0 )nits <- maxit
if( itertrace )
print( c(lam, nlogelr, gsize, ninner) )
}
list( "-2LLR" = -2*nlogelr, Pval = 1-pchisq(-2*nlogelr, df=p),
lambda = lam/scale, grad=grad*scale,
hess=t(hess)%*%hess*scale^2, wts=wts1, nits=nits )
}
logelr <- function( x, mu, lam ){
x <- as.matrix(x)
n <- nrow(x)
p <- ncol(x)
if( n <= p )
stop("Need more observations than variables in logelr.")
mu <- as.vector(mu)
if( length(mu) != p )
stop("Length of mean doesn't match number of variables in logelr.")
z <- t( t(x) -mu )
arg <- 1 + z %*% lam
return( - sum( llog(arg,1/n) ) )
}
#
# The function llog() is equal to the natural
# logarithm on the interval from eps >0 to infinity.
# Between -infinity and eps, llog() is a quadratic.
# llogp() and llogpp() are the first two derivatives
# of llog(). All three functions are continuous
# across the "knot" at eps.
#
# A variation with a second knot at a large value
# M did not appear to work as well.
#
# The cutoff point, eps, is usually 1/n, where n
# is the number of observations. Unless n is extraordinarily
# large, dividing by eps is not expected to cause numerical
# difficulty.
#
llog <- function( z, eps ){
ans <- z
avoidNA <- !is.na(z)
lo <- (z<eps) & avoidNA ### added 3/2012
ans[ lo ] <- log(eps) - 1.5 + 2*z[lo]/eps - 0.5*(z[lo]/eps)^2
ans[ !lo ] <- log( z[!lo] )
ans
}
llogp <- function( z, eps ){
ans <- z
avoidNA <- !is.na(z) ###added 3/2012
lo <- (z<eps) & avoidNA
ans[ lo ] <- 2.0/eps - z[lo]/eps^2
ans[ !lo ] <- 1/z[!lo]
ans
}
llogpp <- function( z, eps ){
ans <- z
avoidNA <- !is.na(z)
lo <- (z<eps) & avoidNA ### added same avoidNA as above
ans[ lo ] <- -1.0/eps^2
ans[ !lo ] <- -1.0/z[!lo]^2
ans
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.