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AI-GEOSTATS: when is spatial autocorrelation important?

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  • William Thayer
    I am posing two questions to the list: An open-ended question that I hope will spark some discussion, and a specific question regarding a project that I am
    Message 1 of 1 , Jun 10 5:57 AM
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      I am posing two questions to the list: An open-ended question that I hope
      will spark some discussion, and a specific question regarding a project
      that I am currently working on.

      The open ended question: When estimating a parameter of a spatial
      distribution (e.g., the mean), or when comparing estimates made for two or
      more geographic regions, when is it important to consider spatial
      autocorrelation ? The specific question: An example of the latter of
      immediate interest to me involves testing the rates at which air samples
      collected in ___ census block groups fail a health-based benchmark. One
      of my tasks is to determine if these rates are homogeneous across the
      census block groups that are located within the study area. Would it be
      valid to simply compare the rates among the census block groups using a
      Chi-square test, even if the rates show spatial autocorrelation, provided
      the data is from a random sample?

      In addition to the lattice data described above, I also have event data
      that represent multiple observations of pass/fail tests for the same
      locations (i.e., each location was cleaned and tested until a 'passing'
      result was obtained). In a 'non-spatial' data analysis framework, I
      planned to fit a geometric distribution to this data to estimate the
      overall pass/fail rate for the entire study area. If the sample size is
      sufficient, I would also like to fit a geometric distribution to each
      census block group (or some other sub-region of the study area) and then
      test for differences in the geometric distribution across the census block
      groups.

      Are 'non-spatial' methods valid if the data were collected using random
      sampling methods? For example, there is some literature (e.g., Brus and de
      Gruijter, 1997; Cressie, 1996) that argues 'non-spatial' methods provide
      valid estimates of the mean, provided the data were collected using random
      sampling methods. The authors argue that the 'independent' of the familiar
      'i.i.d' assumption is satisfied by the random selection method; i.e., its a
      characteristic of the sampling plan, not the variable (or
      attribute). [Brus and de Gruijter (1997) and Cressie ( 1996) both found
      the spatial methods were more efficient for small spatial domains (small
      relative to the number of available observations), while the non-spatial
      methods were more efficient for large spatial domains.] Any comments on this?

      If the data were not gathered using random sampling methods (they were
      not!), do the spatial methods tend to be more robust to the random sampling
      assumption than 'non-spatial methods'?

      I look forward to hearing your responses. I would really appreciate
      references!

      Best regards,
      Bill


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