Re: [R] faster GLS code

Date: Thu, 07 Jan 2010 14:06:34 -0500

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') .

# 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.

Assistant Professor,
Division of Geriatric Medicine and Gerontology School of Medicine
Johns Hopkins University

Ph. (410) 502-2619

• 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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