[R-sig-Geo] lagsarlm with simulated data

[Roger Bivand]

On Mon, 16 Aug 2010, Malcolm Fairbrother wrote:

> Dear list,
>
> I am running some simulations, trying to use lagsarlm (from the spdep 
> package) to recover the parameters used to generate the data. In a basic 
> simulation I am running, I am finding that I am able to recover rho 
> almost perfectly, and all but one of the betas perfectly. However, the 
> beta attached to the constant is substantially biased, for reasons I 
> cannot understand.
>
> The code I am using is below. The spatial weights matrix is from the 48 
> contiguous U.S. states (rows sum to 1). Can anyone see where I am going 
> wrong? Or is the biased B0 coefficient somehow a consequence of the 
> particular neighbourhood structure I'm using? Any help or tips would be 
> much appreciated.

Malcolm,

You didn't set a seed, so I can't reproduce this exactly, but I think that 
the mean of e will be added to your constant, won't it?

n <- 48
e <- matrix(rnorm(n*1000, mean=0, sd=4), 1000, n)
summary(apply(e, 1, mean))

Could you do a scale(e, center=TRUE, scale=FALSE) to force it to mean 
zero?

Hope this helps,

Roger

>
> - Malcolm
>
>
>> n <- dim(W)[1] # sample size
>> Bs <- c(2, 5, 3, -2) # vector of Beta coefficients
>> rho <- 0.2 # set autocorrelation coefficient
>> bres <- matrix(NA, nrow=1000, ncol=5)
>> for (i in 1:1000) {
> + e <- rnorm(n, mean=0, sd=4)
> + X1 <- rnorm(n, 4, 2) # create some independent variables
> + X2 <- rnorm(n, 2, 2)
> + X3 <- rnorm(n, -3, 1)
> + X <- cbind(rep(1, n), X1, X2, X3)
> + y <- (solve(diag(n)-rho*W)) %*% ((X%*%Bs)+e) # generate lagged Ys
> + data <- as.data.frame(cbind(y, X))
> + lagmod <- lagsarlm(y ~ X1 + X2 + X3, data=data, oxw.listw1)
> + bres[i,] <- coefficients(lagmod)
> + }
>> apply(bres, 2, mean)
> [1]  0.1876292  2.6275783  4.9897827  3.0060831 -1.9883803
>> apply(bres, 2, median)
> [1]  0.1907057  2.4000895  4.9887496  3.0043258 -2.0076960
>
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-- 
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Helleveien 30, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no