# Re: Fwd: st: Monte Carlo with preset spatial autocorrelation

 From Austin Nichols To statalist@hsphsun2.harvard.edu Subject Re: Fwd: st: Monte Carlo with preset spatial autocorrelation Date Mon, 11 May 2009 17:05:01 -0400

```Susan Olivia <olivia@primal.ucdavis.edu>:
Yes, I gathered you had a weight matrix, but what is it?  Here's an
example with an identity matrix which trivially satisfies your
description of your weight matrix (here, none of the 200 obs created
are neighbors):

mat c=I(200)
drawnorm v1-v200, corr(c) n(1) seed(1) clear
g i=_n
qui reshape long v, i(i)
keep v

Obviously, this is a silly example, since -drawnorm v, n(200)- would
get there in one; but a different matrix c will produce data with very
different properties. You also don't specify if the simulated data are
supposed to be normal, or exhibit any particular properties.  You
won't get much programming advice unless you can specify a particular
problem, with details...

On Mon, May 11, 2009 at 4:30 PM, Susan Olivia <olivia@primal.ucdavis.edu> wrote:
> Thanks Austin.
>
> Glad to know that it's feasible to do this.
>
> My pre-determined weighting matrix will be an nxn positive
> symmetric matrix in which for non-neighbors, w[i,j]= 0 while
> w[i,j]=1 or a function of inverse distance w[i,j] = 1/d[i,j]
> for neighbors, where d[i,j] is the distance between
> observation i and j.
>
>
> Susan
>
>
>
>
>> ---------- Forwarded message ----------
>> From: Austin Nichols <austinnichols@gmail.com>
>> Date: Mon, May 11, 2009 at 12:49 PM
>> Subject: Re: st: Monte Carlo with preset spatial
>> autocorrelation To: statalist@hsphsun2.harvard.edu
>>
>>
>> Susan Olivia <olivia@primal.ucdavis.edu>:
>> Note that the top of that page says the "FAQ is for users
>> of Stata 6, an older version of Stata. It is not relevant
>> modern equivalent.  If you can give the relevant matrix of
>> correlations or covariances, the rest is easy.  What does
>> your "pre-determined weighting matrix" look like?
>>
>> On Mon, May 11, 2009 at 3:39 PM, Susan Olivia
>> <olivia@primal.ucdavis.edu> wrote:
>> > Dear Stata list,
>> >
>> > I am wondering whether it is possible to generate
>> > artificial data with a given strength of spatial
>> > autocorrelation (for a pre-determined weighting matrix)?
>> >
>> > I found on the STATA archive that Bill Gould wrote some
>> > code about generating a random variable with a given
>> > correlation structure. Here's the url:
>> >
>> > http://www.stata.com/support/faqs/stat/mvnorm.html
>> >
>> > But to do this in a spatial context would seem to be
>> > more complicated given that the spatial autocorrelation
>> > will depend not not only on the own and neighboring
>> > values, but also how far apart they are place.
>> >
>> > If I can get any programming tips on this, much
>> appreciated. >
>> > Thanks,
>> >
>> > Susan
>> *

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