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Re: AI-GEOSTATS: model selection

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  • Marta Rufino
    Dear collegues, Hear is the answer to my email... (I send it before, but we had anemail problem and it did not go. Sory by the delay) thank you all Best wishes
    Message 1 of 3 , Oct 8, 2002
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      Dear collegues,

      Hear is the answer to my email... (I send it before, but we had anemail
      problem and it did not go. Sory by the delay)

      thank you all
      Best wishes

      At 10:07 03/10/02 +0200, you wrote:
      >Dear collegues,
      >I have another doubt....
      >When we have several possible models (with different covariates as an
      >external trend), how doi we decide which one is the most proper one to use
      >(doing the variograms and kriging).
      >Do we simply look at the value of the minimising function (the lowest would
      >be the best)?
      >Do we look at percentage of the spatial variance explained by the model?
      >Do we look at the lowest C (sill+nugget)?
      >Can you help me?
      >thank you
      Hi Marta,

      if you have several possible covariates it is worth you while selecting the
      best correlated. This can be a statistical measure or in the case of
      external drift a clear physical relationship (for example rainfall and
      elevation are often linearly related, but a clear statistical relationship
      may not be observable). Be parsimonious, use as few variables as possible.

      In any case the external drift (or trend) should have a spatial structure
      that is smoother than the variable of interest. Hans Wackernagels book,
      "Multivariate Geostatistics" provides a good overview,

      Then of course there are validation tests that can help you choose such as
      X-validation, but a rationale choice in the first instance can save a lot
      of time testing different models.

      Benjamin Warr

      Research Fellow

      Centre for the Management of Environmental Resource(CMER)
      Boulevard de Constance,
      77305 Fontainebleau Cedex,


      You can use the Cressie goodness of fit statistic to
      assess relative merits of various models.

      You should also look at the cross validation
      statistics to see which gives you closest to the ideal
      behaviour and best correlation between estimated and
      actual values.

      Better estimates (in the real sense) are achieved with
      models in which the nugget effect/sill ratio is a
      minimum and where the range of influence is longest
      (in that order of priority). The total sill is
      virtually irrelevant in determining your kriging
      weights and only affects the kriging variance as a
      constant factor. Unless, of course, you are doing
      lognormal kriging where the total sill is vital to the
      back transform.

      Isobel Clark

      __ Estimada Marta:

      Te escribo fuera de la lista para hacerlo en español, lo cual creo que
      puede ser más ágil para ambos.

      Para la elección de un modelo determinado no debes basarte en índices
      estadísticos. La geoestadística no es la aplicación de la estadística a
      diversos campos. Por ello, debes elegir un modelo que se ajuste bien a tus
      datos y que expliquen razonablemente la posible distribución de los mismos.
      Para ello debes realizar consideraciones subjetivas (elegir un modelo que
      se ajuste más o menos a tus datos) y basarte en la experiencia previa (si
      existe). O sea, si en un trabajo anterior un modelo se ajustó bien a los
      datos, no hay razón para considerar otro modelo distinto.

      Otra cosa que puede ser útil es conocer si la distribución de la
      variable estudiada es más o menos continua. En ese caso es conveniente
      ajustar un tipo de modelo u otro (gaussiano o esférico, por ejemplo).

      Si te interesa, tengo en prensa un libro sobre geoestadística lineal,
      el cual podría enviarte vía mail.

      Un saludo.

      Dear Marta,
      Have a look at reduced mean error and reduced variance.
      In my opinion, these are indeed good indicators of approppriate models.
      By the way, I would like to learn if you have GS+ software. If you have,
      what is the version?
      Looking forward to hearing from you, soon.
      Yours Sincerely,
      Dr. Mahmut CETIN

      Hi marta

      If you fit the models usig maximum likelihood you can use the AIC or BIC
      as a criteria to choose the model.
      AIC: Akaike information criteria
      BIC: Baeysian information criteria

      The function likfit() in geoR returns them both


      I don't think there is going to be an absolute answer to your question.
      However I suggest that you look at the following:

      1. Do you have data at the same number of locations for all of the possible
      covariates? (more data locations is better)

      2. The match between data locations for possible covariates and data
      locations for the principal variable.

      3. Standard regression diagnostics when fitting the principal variable to
      each of the possible covariates

      4. Since you are going to be using the "residuals" for the principal
      variable to estimate and model the variogram (or covariance), how does the
      fitting compare using each of the different possible covariates? For
      example, there are multiple cross-validation statistics you can use

      5. Of course you also want to consider which of the different possible
      covariates makes better sense , i.e., is the relationship between the
      possible covariate and the principal variable simply one of correlation or
      is there evidence or theory or reason to believe that there is something
      closer to a causual relationship.

      6. Are the possible covariates interdependent?

      Donald E. Myers



      Marta Rufino

      Centre Mediterrani d'Investigacions Marines i Ambientals
      (CMIMA). CSIC
      Passeig Maritim 37-49
      08003 BARCELONA

      Tfno:34 93 230 95 40
      Tfax:34 93 230 95 55


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