On Thu, 7 Jan 2010, Ravi Varadhan wrote:
Try this:
X <- kronecker(diag(1,3),x)
Y <- c(y) # stack the y in a vector
# residual covariance matrix for each observation
covar <- kronecker(sigma,diag(1,N))
csig <- chol2inv(covar)
betam2 <- ginv(csig %*% X) %*% csig %*% Y
This is more than 2 times faster than your code (however, it doesn't compute
`betav') .
Faster still (by a wide margin) if X will truly be of that form:
B <- coef(lm(y~0+.,as.data.frame(x)))
all.equal( as.vector((B)), as.vector(betam))
[1] TRUE
When X is of that form, the covariance matrix drops out of the
computation.
:)
Chuck
Here is a timing comparison:
# Your method
# GLS betas covariance matrix
system.time({
inv.sigma <- solve(covar)
betav <- solve(t(X)%*%inv.sigma%*%X)
# GLS mean parameter estimates
betam <- betav%*%t(X)%*%inv.sigma%*%Y
})
# New method
system.time({
csig <- chol2inv(covar)
betam2 <- ginv(csig %*% X) %*% csig %*% Y
})
all.equal(betam, betam2)
# GLS betas covariance matrix
system.time({
+ inv.sigma <- solve(covar)
+ betav <- solve(t(X)%*%inv.sigma%*%X)
+
+ # GLS mean parameter estimates
+ betam <- betav%*%t(X)%*%inv.sigma%*%Y
+ })
user system elapsed
1.14 0.51 1.76
system.time({
+ csig <- chol2inv(covar)
+ betam2 <- ginv(csig %*% X) %*% csig %*% Y
+ })
user system elapsed
0.47 0.08 0.61
all.equal(betam, betam2)
[1] TRUE
Hope this helps,
Ravi.
____________________________________________________________________
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University
Ph. (410) 502-2619
email: rvarad...@jhmi.edu
----- Original Message -----
From: Carlo Fezzi <c.fe...@uea.ac.uk>
Date: Thursday, January 7, 2010 12:13 pm
Subject: [R] faster GLS code
To: r-help@r-project.org
Dear helpers,
I wrote a code which estimates a multi-equation model with generalized
least squares (GLS). I can use GLS because I know the covariance
matrix of
the residuals a priori. However, it is a bit slow and I wonder if anybody
would be able to point out a way to make it faster (it is part of a bigger
code and needs to run several times).
Any suggestion would be greatly appreciated.
Carlo
***************************************
Carlo Fezzi
Senior Research Associate
Centre for Social and Economic Research
on the Global Environment (CSERGE),
School of Environmental Sciences,
University of East Anglia,
Norwich, NR4 7TJ
United Kingdom.
email: c.fe...@uea.ac.uk
***************************************
Here is an example with 3 equations and 2 exogenous variables:
----- start code ------
N <- 1000 # number of observations
library(MASS)
## parameters ##
# eq. 1
b10 <- 7; b11 <- 2; b12 <- -1
# eq. 2
b20 <- 5; b21 <- -2; b22 <- 1
# eq.3
b30 <- 1; b31 <- 5; b32 <- 2
# exogenous variables
x1 <- runif(min=-10,max=10,N)
x2 <- runif(min=-5,max=5,N)
# residual covariance matrix
sigma <- matrix(c(2,1,0.7,1,1.5,0.5,0.7,0.5,2),3,3)
# residuals
r <- mvrnorm(N,mu=rep(0,3), Sigma=sigma)
# endogenous variables
y1 <- b10 + b11 * x1 + b12*x2 + r[,1]
y2 <- b20 + b21 * x1 + b22*x2 + r[,2]
y3 <- b30 + b31 * x1 + b32*x2 + r[,3]
y <- cbind(y1,y2,y3) # matrix of endogenous
x <- cbind(1,x1, x2) # matrix of exogenous
#### MODEL ESTIMATION ###
# build the big X matrix needed for GLS estimation:
X <- kronecker(diag(1,3),x)
Y <- c(y) # stack the y in a vector
# residual covariance matrix for each observation
covar <- kronecker(sigma,diag(1,N))
# GLS betas covariance matrix
inv.sigma <- solve(covar)
betav <- solve(t(X)%*%inv.sigma%*%X)
# GLS mean parameter estimates
betam <- betav%*%t(X)%*%inv.sigma%*%Y
----- end of code ----
______________________________________________
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PLEASE do read the posting guide
and provide commented, minimal, self-contained, reproducible code.
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Charles C. Berry (858) 534-2098
Dept of Family/Preventive Medicine
E mailto:cbe...@tajo.ucsd.edu UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
