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AI-GEOSTATS: spatial GLMM with nested correlation structure

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  • John Jansen
    Hello all -- I m in the midst of modeling the distribution of ice-hauling seals in relation to covariates such as day of year (DOY) and ice cover (ICE.COV).
    Message 1 of 4 , Feb 4, 2004
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      Hello all -- I'm in the midst of modeling the distribution of
      ice-hauling seals in relation to covariates such as day of year (DOY)
      and ice cover (ICE.COV). By strip-transect sampling on 20 separate
      days, I have created a lattice of cells containing seal counts and the
      corresponding covariate measures. To remove a significant north-south
      trend in seal counts, I extracted the residuals from a GAM loess smooth
      of seal counts on the lat/long variables. Modeling the residuals, I
      arrived at the following S+ best fit (using AIC):

      glmmPQL(sealsum.gamfit ~ ICE.COV * DOY * SHIPACT2, random = ~ 1| DOY,
      family = poisson, data = yakgrid.fit, correlation = corGaus(form = ~
      lat.yak + lon.yak | DOY), verbose = T))

      I determined that a gaussian variogram best fit the spatial
      autocorrelation by exploring the data in Surfer, VarioWin, and S+. But
      I have encountered a significant degree of both geometric and zonal
      anisotropy. I believe the anisotropy is real as there are several
      reasonable hypothesis that explain its presence which have to do with
      the seals concentrating in a stream of ice, i.e., creating
      discontinuities in variance and correlation within the study area.
      Though complicated, I have been able to model the autocorrelation (in
      VarioWin) by nesting two spatial structures (both Gaussian)
      corresponding to the directions of maximum and minimum continuity. The
      problem is that I now need to transport this nested model into the S+
      spatial GLMM framework. The avenues I have explored thus far are:

      1) create a new corStruct class in S+ that corresponds to a
      gaussian-gaussian nested model. Problem: I have been unable to find
      any documentation on how to create a new class though the online help
      indicates that it is possible "by specifying a constructor function and
      methods for the functions corMatrix and coef".

      2) transforming/weighting the coordinates prior to running the model.
      Problem: though a geometric transform of the coordinates is
      straightforward it is less obvious how to conduct such a transform using
      a nested model.

      It may be I'm forcing a square peg (nested model) in a round hole (S+
      spatial GLMM), but I'm hoping someone out there has done this in S+
      before and can pass along their experience. Otherwise, I'm soliciting
      the wisdom of those who know where to find the square hole that matches
      my square peg, i.e., other software or techniques that allow one to
      account for spatial correlation with nested structures with the main
      focus of modeling the relation of animals to their environment. Much
      gratitude to any assistance. Thanks, John Jansen


      --
      John K. Jansen
      Wildlife Biologist
      National Marine Mammal Laboratory
      NOAA Fisheries
      7600 Sand Point Way N.E. Bldg 4
      Seattle, WA 98115-6349
      voice: 206.526.4027
      fax: 206.526.6615
      email: John.Jansen@...



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    • Steven Citron-Pousty
      A simple suggestion is to see how much worse your model fit becomes with a standard variogram model. Having used S+ for this kind of work a while ago I am
      Message 2 of 4 , Feb 4, 2004
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        A simple suggestion is to see how much "worse" your model fit becomes
        with a "standard" variogram model. Having used S+ for this kind of work
        a while ago I am not sure how straightforward it will be to do a the
        non-standard variogram.

        It looks like this page may help:
        http://www.cas.umt.edu/math/graham/math595/math595.html
        google is your friend
        Steve

        John Jansen wrote:

        >Hello all -- I'm in the midst of modeling the distribution of
        >ice-hauling seals in relation to covariates such as day of year (DOY)
        >and ice cover (ICE.COV). By strip-transect sampling on 20 separate
        >days, I have created a lattice of cells containing seal counts and the
        >corresponding covariate measures. To remove a significant north-south
        >trend in seal counts, I extracted the residuals from a GAM loess smooth
        >of seal counts on the lat/long variables. Modeling the residuals, I
        >arrived at the following S+ best fit (using AIC):
        >
        >glmmPQL(sealsum.gamfit ~ ICE.COV * DOY * SHIPACT2, random = ~ 1| DOY,
        >family = poisson, data = yakgrid.fit, correlation = corGaus(form = ~
        >lat.yak + lon.yak | DOY), verbose = T))
        >
        >I determined that a gaussian variogram best fit the spatial
        >autocorrelation by exploring the data in Surfer, VarioWin, and S+. But
        >I have encountered a significant degree of both geometric and zonal
        >anisotropy. I believe the anisotropy is real as there are several
        >reasonable hypothesis that explain its presence which have to do with
        >the seals concentrating in a stream of ice, i.e., creating
        >discontinuities in variance and correlation within the study area.
        >Though complicated, I have been able to model the autocorrelation (in
        >VarioWin) by nesting two spatial structures (both Gaussian)
        >corresponding to the directions of maximum and minimum continuity. The
        >problem is that I now need to transport this nested model into the S+
        >spatial GLMM framework. The avenues I have explored thus far are:
        >
        >1) create a new corStruct class in S+ that corresponds to a
        >gaussian-gaussian nested model. Problem: I have been unable to find
        >any documentation on how to create a new class though the online help
        >indicates that it is possible "by specifying a constructor function and
        >methods for the functions corMatrix and coef".
        >
        >2) transforming/weighting the coordinates prior to running the model.
        >Problem: though a geometric transform of the coordinates is
        >straightforward it is less obvious how to conduct such a transform using
        >a nested model.
        >
        >It may be I'm forcing a square peg (nested model) in a round hole (S+
        >spatial GLMM), but I'm hoping someone out there has done this in S+
        >before and can pass along their experience. Otherwise, I'm soliciting
        >the wisdom of those who know where to find the square hole that matches
        >my square peg, i.e., other software or techniques that allow one to
        >account for spatial correlation with nested structures with the main
        >focus of modeling the relation of animals to their environment. Much
        >gratitude to any assistance. Thanks, John Jansen
        >
        >
        >--
        >John K. Jansen
        >Wildlife Biologist
        >National Marine Mammal Laboratory
        >NOAA Fisheries
        >7600 Sand Point Way N.E. Bldg 4
        >Seattle, WA 98115-6349
        >voice: 206.526.4027
        >fax: 206.526.6615
        >email: John.Jansen@...
        >
        >
        >
        >--
        >* To post a message to the list, send it to ai-geostats@...
        >* As a general service to the users, please remember to post a summary of any useful responses to your questions.
        >* To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
        >* Support to the list is provided at http://www.ai-geostats.org
        >
        >


        --
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      • Edzer J. Pebesma
        John, the gstat R package/S-Plus library, found at http://www.gstat.org/s.html does provide nested variograms, each having their own anisotropy parameters.
        Message 3 of 4 , Feb 5, 2004
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          John, the gstat R package/S-Plus library, found at

          http://www.gstat.org/s.html

          does provide nested variograms, each having their
          own anisotropy parameters. However, it does not
          do a fully integrated variogram parameter estimation
          in a Poisson framework; you'd have to work with
          residuals. More specificly, it does not fit anisotropy
          ratios nor directions; only sills and ranges.
          --
          Edzer

          John Jansen wrote:

          >Hello all -- I'm in the midst of modeling the distribution of
          >ice-hauling seals in relation to covariates such as day of year (DOY)
          >and ice cover (ICE.COV). By strip-transect sampling on 20 separate
          >days, I have created a lattice of cells containing seal counts and the
          >corresponding covariate measures. To remove a significant north-south
          >trend in seal counts, I extracted the residuals from a GAM loess smooth
          >of seal counts on the lat/long variables. Modeling the residuals, I
          >arrived at the following S+ best fit (using AIC):
          >
          >glmmPQL(sealsum.gamfit ~ ICE.COV * DOY * SHIPACT2, random = ~ 1| DOY,
          >family = poisson, data = yakgrid.fit, correlation = corGaus(form = ~
          >lat.yak + lon.yak | DOY), verbose = T))
          >
          >I determined that a gaussian variogram best fit the spatial
          >autocorrelation by exploring the data in Surfer, VarioWin, and S+. But
          >I have encountered a significant degree of both geometric and zonal
          >anisotropy. I believe the anisotropy is real as there are several
          >reasonable hypothesis that explain its presence which have to do with
          >the seals concentrating in a stream of ice, i.e., creating
          >discontinuities in variance and correlation within the study area.
          >Though complicated, I have been able to model the autocorrelation (in
          >VarioWin) by nesting two spatial structures (both Gaussian)
          >corresponding to the directions of maximum and minimum continuity. The
          >problem is that I now need to transport this nested model into the S+
          >spatial GLMM framework. The avenues I have explored thus far are:
          >
          >1) create a new corStruct class in S+ that corresponds to a
          >gaussian-gaussian nested model. Problem: I have been unable to find
          >any documentation on how to create a new class though the online help
          >indicates that it is possible "by specifying a constructor function and
          >methods for the functions corMatrix and coef".
          >
          >2) transforming/weighting the coordinates prior to running the model.
          >Problem: though a geometric transform of the coordinates is
          >straightforward it is less obvious how to conduct such a transform using
          >a nested model.
          >
          >It may be I'm forcing a square peg (nested model) in a round hole (S+
          >spatial GLMM), but I'm hoping someone out there has done this in S+
          >before and can pass along their experience. Otherwise, I'm soliciting
          >the wisdom of those who know where to find the square hole that matches
          >my square peg, i.e., other software or techniques that allow one to
          >account for spatial correlation with nested structures with the main
          >focus of modeling the relation of animals to their environment. Much
          >gratitude to any assistance. Thanks, John Jansen
          >
          >
          >--
          >John K. Jansen
          >Wildlife Biologist
          >National Marine Mammal Laboratory
          >NOAA Fisheries
          >7600 Sand Point Way N.E. Bldg 4
          >Seattle, WA 98115-6349
          >voice: 206.526.4027
          >fax: 206.526.6615
          >email: John.Jansen@...
          >
          >
          >
          >--
          >* To post a message to the list, send it to ai-geostats@...
          >* As a general service to the users, please remember to post a summary of any useful responses to your questions.
          >* To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
          >* Support to the list is provided at http://www.ai-geostats.org
          >
          >


          --
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          * As a general service to the users, please remember to post a summary of any useful responses to your questions.
          * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
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        • Brian R Gray
          John: if by nested you mean hierarchical and if what you are working with (some function of what originally were counts) may ostensibly be viewed as normal,
          Message 4 of 4 , Feb 5, 2004
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            John: if by "nested" you mean hierarchical and if what you are working
            with (some function of what originally were counts) may ostensibly be
            viewed as normal, then you should be able to do this in SAS' PROC MIXED.
            if your data remain counts then you may be able to do the same in the SAS
            macro glimmix--under an over(under?)-dispersed Poisson assumption. glimmix
            relies on a pseudolikelihood assumption, and relies on MIXED to analyze
            pseudodata. as always, fitting complex structures may require more data
            (at possibly multiple scales) than ecologists may have. brian

            ****************************************************************
            Brian Gray, Ph.D.
            USGS Upper Midwest Environmental Sciences Center
            2630 Fanta Reed Road, La Crosse, WI 54602
            608-783-7550 ext 19 - Onalaska campus or
            608-781-6234 - La Crosse campus
            fax 608-783-8058
            brgray@...
            *****************************************************************


            |---------+---------------------------->
            | | "Edzer J. |
            | | Pebesma" |
            | | <e.pebesma@geog.u|
            | | u.nl> |
            | | Sent by: |
            | | ai-geostats-list@|
            | | unil.ch |
            | | |
            | | |
            | | 02/05/2004 02:15 |
            | | AM |
            | | Please respond to|
            | | "Edzer J. |
            | | Pebesma" |
            | | |
            |---------+---------------------------->
            >--------------------------------------------------------------------------------------------------------------------------------------------------|
            | |
            | To: John Jansen <John.Jansen@...> |
            | cc: ai-geostats@... |
            | Subject: Re: AI-GEOSTATS: spatial GLMM with nested correlation structure |
            >--------------------------------------------------------------------------------------------------------------------------------------------------|




            John, the gstat R package/S-Plus library, found at

            http://www.gstat.org/s.html

            does provide nested variograms, each having their
            own anisotropy parameters. However, it does not
            do a fully integrated variogram parameter estimation
            in a Poisson framework; you'd have to work with
            residuals. More specificly, it does not fit anisotropy
            ratios nor directions; only sills and ranges.
            --
            Edzer

            John Jansen wrote:

            >Hello all -- I'm in the midst of modeling the distribution of
            >ice-hauling seals in relation to covariates such as day of year (DOY)
            >and ice cover (ICE.COV). By strip-transect sampling on 20 separate
            >days, I have created a lattice of cells containing seal counts and the
            >corresponding covariate measures. To remove a significant north-south
            >trend in seal counts, I extracted the residuals from a GAM loess smooth
            >of seal counts on the lat/long variables. Modeling the residuals, I
            >arrived at the following S+ best fit (using AIC):
            >
            >glmmPQL(sealsum.gamfit ~ ICE.COV * DOY * SHIPACT2, random = ~ 1| DOY,
            >family = poisson, data = yakgrid.fit, correlation = corGaus(form
            = ~
            >
            >I determined that a gaussian variogram best fit the spatial
            >autocorrelation by exploring the data in Surfer, VarioWin, and S+. But
            >I have encountered a significant degree of both geometric and zonal
            >anisotropy. I believe the anisotropy is real as there are several
            >reasonable hypothesis that explain its presence which have to do with
            >the seals concentrating in a stream of ice, i.e., creating
            >discontinuities in variance and correlation within the study area.
            >Though complicated, I have been able to model the autocorrelation (in
            >VarioWin) by nesting two spatial structures (both Gaussian)
            >corresponding to the directions of maximum and minimum continuity. The
            >problem is that I now need to transport this nested model into the S+
            >spatial GLMM framework. The avenues I have explored thus far are:
            >
            >1) create a new corStruct class in S+ that corresponds to a
            >gaussian-gaussian nested model. Problem: I have been unable to find
            >any documentation on how to create a new class though the online help
            >indicates that it is possible "by specifying a constructor function and
            >methods for the functions corMatrix and coef".
            >
            >2) transforming/weighting the coordinates prior to running the model.
            >Problem: though a geometric transform of the coordinates is
            >straightforward it is less obvious how to conduct such a transform using
            >a nested model.
            >
            >It may be I'm forcing a square peg (nested model) in a round hole (S+
            >spatial GLMM), but I'm hoping someone out there has done this in S+
            >before and can pass along their experience. Otherwise, I'm soliciting
            >the wisdom of those who know where to find the square hole that matches
            >my square peg, i.e., other software or techniques that allow one to
            >account for spatial correlation with nested structures with the main
            >focus of modeling the relation of animals to their environment. Much
            >gratitude to any assistance. Thanks, John Jansen
            >
            >
            >--
            >John K. Jansen
            >Wildlife Biologist
            >National Marine Mammal Laboratory
            >NOAA Fisheries
            >7600 Sand Point Way N.E. Bldg 4
            >Seattle, WA 98115-6349
            >voice: 206.526.4027
            >fax: 206.526.6615
            >email: John.Jansen@...
            >
            >
            >
            >--
            >* To post a message to the list, send it to ai-geostats@...
            >* As a general service to the users, please remember to post a summary of
            any useful responses to your questions.
            >* To unsubscribe, send an email to majordomo@... with no subject and
            "unsubscribe ai-geostats" followed by "end" on the next line in the message
            body. DO NOT SEND Subscribe/Unsubscribe requests to the list
            >* Support to the list is provided at http://www.ai-geostats.org
            >
            >


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