- Jul 23, 2001Dear all,

Many thanks to Brian Gray, Darla Munroe, Carlos Carroll, Wayne

Thogmartin, who replied to the question below...I've pasted in

responses FYI.

Basically, it seems as if there is no off-the-peg solution to this

problem. I'm going to look into the Gotway & Stroup paper, and also

look at transforming the data to utilise linear regression instead. The

response variable is counts of deaths, so I reckon I might get away

with age-sex specific/standardised mortality rates to use as a linear

outcome.

Cheers

Ben

Original question:

> I'm running poisson regressions for a large number of small areas

1.

> (several thousand contiguous polygons) - predicting counts of events

> with several predictor variables for each small area. I'd like to be

> able to adjust these models to account for spatial autocorrelation.

> Does anyone know of software (ideally free/cheap) that will do this in

> a reasonably straightforward way? Either stand-alone or as an add-on to

> Arc/info or arcview. I can also use Stata, SAS, SPSS etc.

How are you adjusting your p-values to account for the multiple

regressions--each with a potential for a Type I error/s? And, how do

you determine which points are in which polygon: if they are

spatially-correlated, could information associated with points be

shared across polygons? sorry for the questions, but my interest is in

modeling spatially-correlated nonnormal data. frankly, I haven't seen

extensions to multiple, practically-simultaneous regressions.

depending on the answers to the above questions, you might enjoy

reading Gotway, C.A. and W.W. Stroup. 1997. A generalized linear model

approach to spatial data analysis and prediction. Journal of

Agricultural, Biological, and Environmental Statistics 2: 157-178..

they examine issues pertaining to the analysis of nonnormal data under a

generalized linear model context.

_________________________________________

2.

You might want to contact Dan Griffith, Dept of Geography at Syracuse

University - he is working on an estimator for this exact case.

As far as I know, there is no built-in model for spatial

autocorrelation in a poisson regression (though there may be some code

out there - probably for GAUSS or something - you'd have to code the

autocorrelation into the maximum likelihood estimator - pretty sticky

stuff

__________________________________________

3.

Cressie indicates in his book on spatial statistics that an

"auto-Poisson" procedure (a Poisson regression incorporating spatial

autocorrelation) is infeasible. There are linear methods available in

Splus with the Spatial Statistics add-on that allow you to include

spatial autocorrelation in your models, but obviously a transformation

of the data would first be required.

___________________________________________

4.

You may be able to implement this in BUGS. You could ask the BUGS

listserv:

BUGS@...

or check the bugs WWW site

http://www.mrc-bsu.cam.ac.uk/bugs

__________________________________________

5.

Just to be a little more clear: spatial effects in qualitative data

regression models are UGLY UGLY things...and no one has many good

solutions yet (though a few people are working furiously on it).

Basically, in any sort of qualitative data model, such as a possion

model - where your observed dependent variable is a count of a

occurrence/nonoccurence of some event - the observed process is not

where the spatial effect would/should be modeled. These regressions

are called latent, because there is some underlying process (that we do

not observe) that is generating the qualitative outcome.

For this reason, any spatial autocorrelation would be part of this

latent, unobserved process, not necessarily corresponding one-to-one to

the observed outcome.

Kurt Beron and Wim Vijverberg of U Texas, Dallas, have a chapter coming

out in the new Anselin spatial econometrics book (should come out this

year), New Advances in Spatial Econometrics, that has a really good and

careful review of spatial effects in probit models, and how difficult it

is to specify a full covariance structure taking these into account.

As I mentioned, Dan Griffith of Syracuse is working on poisson models.

I think Harry Kelejian (Dept of Economics, Maryland) has developed a

TEST for autocorrelation in possion models (but no correction).

You say you have thousands of polygons? YIKES. Beron and Vijverberg

developed a spatial probit estimator for 48 observations (or something

like that), and it takes several hours to run. The nXn weighting

structure/incidental parameter problem makes it very hard to identify

anything that big.

___________________________

In response to 5:

I wonder if probit and Poisson are here confused? Continuous outcomes

are typically categorized using categories rather than counts. This

approach doesn't appear to describe Ben's case. Further, I am not sure

why a latent process must be assumed.

Counts are theoretically Poisson only if they meet a certain number of

assumptions/postulates. Autocorrelation is a violation, as I recall,

of these postulates. However, over- or underdispersion arising from

spatial autocorrelation may, in an estimation context, be handled from

a number of perspectives, including generalized estimating equations

and generalized linear mixed models. The negative binomial distribution

may also be used to model count data. I recommend Gotway, C.A. and

W.W. Stroup. 1997. A generalized linear model approach to spatial data

analysis and prediction. Journal of Agricultural, Biological, and

Environmental Statistics 2: 157-178.. they examine issues pertaining

to the analysis of nonnormal data under a generalized linear model

context.

-------------------------

Ben Wheeler

MRC Research Student

Department of Social Medicine

University of Bristol

Tel. (0117) 928 7288

e-mail ben.wheeler@...

-------------------------

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