faster GLS code

Thu, Jan 7, 2010 11:06 AM

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') . 

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)

+ 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

+ csig <- chol2inv(covar)
+ betam2 <- ginv(csig %*% X) %*% csig %*% Y
+ })
   user  system elapsed 
   0.47    0.08    0.61

[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: rvaradhan at jhmi.edu


----- Original Message -----
From: Carlo Fezzi <c.fezzi at uea.ac.uk>
Date: Thursday, January 7, 2010 12:13 pm
Subject: [R] faster GLS code
To: r-help at 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.fezzi at 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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faster GLS code

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