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AI-GEOSTATS: Spatial poisson regression software?

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  • Ben Wheeler
    Dear all, Please forgive the newbie style question...I ve looked on the website at software listings and can t quite work out what I m after. I m running
    Message 1 of 4 , Jul 19, 2001
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      Dear all,

      Please forgive the newbie style question...I've looked on the website
      at software listings and can't quite work out what I'm after.

      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.

      Any ideas much appreciated,

      Thanks a lot

      Cheers
      Ben


      -------------------------
      Ben Wheeler
      MRC Research Student
      Department of Social Medicine
      University of Bristol
      UK

      e-mail ben.wheeler@...
      -------------------------


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    • Munroe, Darla
      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
      Message 2 of 4 , Jul 19, 2001
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        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).

        Good luck,
        Darla Munroe

        --
        ***************************************
        Darla Munroe, Ph.D.
        Postdoctoral Fellow
        Center for the Study of Institutions,
        Population, and Environmental Change
        Indiana University
        408 N. Indiana
        Bloomington, IN 47408
        dmunroe@...
        php.indiana.edu/~dmunroe




        -----Original Message-----
        From: Ben Wheeler [mailto:Ben.Wheeler@...]
        Sent: Thursday, July 19, 2001 7:49 AM
        To: ai-geostats@...
        Subject: AI-GEOSTATS: Spatial poisson regression software?


        Dear all,

        Please forgive the newbie style question...I've looked on the website
        at software listings and can't quite work out what I'm after.

        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.

        Any ideas much appreciated,

        Thanks a lot

        Cheers
        Ben


        -------------------------
        Ben Wheeler
        MRC Research Student
        Department of Social Medicine
        University of Bristol
        UK

        e-mail ben.wheeler@...
        -------------------------


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      • Ben Wheeler
        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.
        Message 3 of 4 , Jul 23, 2001
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          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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        • Nicholas Lewin-Koh
          Hi Ben, Just one more place to look is R (or Gnu Splus). There is a module on cran for generalized linear mixed models, which is actually a port of the
          Message 4 of 4 , Jul 23, 2001
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            Hi Ben,
            Just one more place to look is R (or Gnu Splus). There is a module on cran
            for generalized linear mixed models, which is actually a port of the
            software (beam) that was used by Clayton and Kaldor 1987 JASA. They use a
            hierarchical modeling approach and get the randome effects distributions
            using mcmc. You can also use bugs to do this as was mentioned in your
            summary.

            In your question I was not sure if you wanted to model the functional
            relationship between your response and predictors or to predict unobserved
            locations. If the former then the glm approach might be the best, if the
            latter than the Gottaway and stroup approach might be better. I recall
            that articale dealt more with prediction. Another article to look at is
            diggle, tawn and moyeed (or some permutation of the names) I think the
            article is called Model Based Geostatistics and is in JRSS A or C,
            whichever is applied statistics. I don't know if they ever distributed
            software for the application, I think the MCMC procedure they used was not
            very stable.

            So the question is what are the goals of this analysis and the methods
            will follow.

            Nicholas

            CH3
            |
            N Nicholas Lewin-Koh
            / \ Dept of Statistics
            N----C C==O Program in Ecology and Evolutionary Biology
            || || | Iowa State University
            || || | Ames, IA 50011
            CH C N--CH3 http://www.public.iastate.edu/~nlewin
            \ / \ / nlewin@...
            N C
            | || Currently
            CH3 O Graphics Lab
            School of Computing
            National University of Singapore
            The Real Part of Coffee kohnicho@...


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