[R-sig-Geo] Simulating variables with predefined correlation and autocorrelation

[Facundo Muñoz]

Dear Amitha,

I'm not sure I understand well your question (but then, I don't know
this Durbin model). From what I quickly looked up it follows this
formulation:

y = \rho W y + \alpha 1_n + X \beta + W X \theta + \varepsilon

where y are the observations (thus, what you are trying to simulate if I
understood correctly), W, X and 1_n are fixed and known matrices, and
the greek letters are the unknown parameters.

For simulating y from this model, you should assign values to the greek
letters and compute:

y = (I_n - \rho W)^{-1} [\alpha 1_n + X \beta + W X \theta + \varepsilon]

Does this help?

ƒacu.-


On 8/21/19 8:52 AM, Amitha Puranik wrote:
> Hello everyone,
>
> I'm trying to simulate a set of variables by specifying correlations. For
> the simulated data, I also want to specify autocorrelations. Basically I am
> trying to simulate data assuming spatial durbin model (a model which
> accounts for autocorrelation in both Y and X). I came across the post
> on ‘*Simulating
> spatially autocorrelated data*’ in R-sig-geo (
> https://stat.ethz.ch/pipermail/r-sig-geo/2011-September/012728.html) where
> similar query was discussed, however the focus there was on generating
> autocorrelated dependent variable.
>
> Can anyone assist me on this? Thanks in advance.
>
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>
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