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316AI-GEOSTATS: Sum: Spatial poisson regression software?

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  • Ben Wheeler
    Jul 23, 2001
    • 0 Attachment
      Dear 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
      > (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.

      1.
      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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