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Karen,<br>
<br>
The approach I have taken to this problem in the past, is to fit a
Poisson - Normal model and use the normal variation in the Poisson
means to capture spatial dependence. Essentially, conditional on the
random effects and predictors, the outcome is assumed to be an
independently drawn Poisson random variable. <br>
<br>
I have seen two, Bayesian approaches to this problem - the spatial
multi-membership model and the conditional autoregressive model - both
impose a spatial structure on the normally distributed error term in
the GLMM, and both can be estimated in WinBugs. There are a couple of
packages in R that enable you to enable you to send data to WinBugs,
but I found some working knowledge of WinBugs to be essential. Of
course, the big challenge is learning MCMC - if you are not familiar
with it already. Luckily, a practical guides to estimating a Poisson
GLMM with spatially correlated normal disturbances are available....For
example, check out the "MCMC estimation in MLwiN" manual on the MlwiN
website...<span class="Apple-style-span"
style="border-collapse: separate; color: rgb(0, 0, 0); font-family: 'Times New Roman'; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><span
class="Apple-style-span"
style="font-family: Tahoma; font-size: 12px; white-space: pre;"><a class="moz-txt-link-freetext" href="http://www.cmm.bristol.ac.uk/MLwiN/download/manuals.shtml">http://www.cmm.bristol.ac.uk/MLwiN/download/manuals.shtml</a>.
<br>
<br>
<br>
</span></span>Short of MCMC, my only other suggestion would be to
estimate and ordinary Poisson GLMM, store the empirical Bayes estimates
for the residuals in a vector, then calculate a Moran's I. I don't
know if the constant variance assumption is reasonable in this setting,
but a low Moran I estimate might convince your readers that your
findings are not unduly influenced by unaccounted for spatial
autocorrelation....<br>
<br>
<br>
On a final note, I regard the Poisson-Normal model as being very
similar to the Negative Binomial model in that both model "extra"
Poisson variability using a continuously distributed random
disturbance. The big difference is that the Poisson - Normal model
generalizes easier to problems like yours...<br>
<br>
hope this helps!<br>
<br>
Sam Field<br>
FPG Child Development Institute<br>
UNC - CH<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
Karen Lamb wrote:
<blockquote cite="mid:4B0E5C88.8030002@sphsu.mrc.ac.uk" type="cite">Hi,
<br>
<br>
I am currently trying to determine a way of assessing whether or not
there is spatial autocorrelation present in my model residuals and was
hoping someone could help me with this.
<br>
<br>
I have information on counts in over six thousand areas, with around
half of the areas found to have a count of zero. I decided to fit a
Zero-Inflated Poisson model and a Negative Binomial as the data is
greatly overdispersed. However, neither of these approaches take into
account the likelihood that there is spatial autocorrelation present in
the data set.
<br>
<br>
I have been searching for the last two weeks to find appropriate
methods to fit a spatial glm model. However, as I am new to spatial
statistical methodology I am finding it difficult to decide how best to
do this. It am not sure that any of the existing R functions are
particularly suitable to my use. I am not interested in prediction as I
have data on a population. I am interested in assessing the
coefficients of variables and whether or not the variables are
significant in determining outcome. I have noticed that a lot of
analyses use a Bayesian approach which may be the way forward.
<br>
<br>
My question, however, relates to the glm models I have fitted. I have
included variables which may explain some of the spatial correlations
such as urban/rural classification. I would like to see if any residual
spatial autocorrelation remains in the model but cannot find a way of
doing this. On searching the R-sig-Geo archives the Morans Test or
Morans I are mentioned. However, I noticed someone had queried using
the moran test in R for residuals from a logistic regression and had
been told that lm.morantest() is available for linear regression but
there is not an alternative for the glm. Has anyone got any suggestions
for how to check my residuals? Are there particular plots that can be
assessed?
<br>
<br>
Thanks for your assistance.
<br>
<br>
Cheers,
<br>
Karen
<br>
<br>
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</blockquote>
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