[R-sig-Geo] Teaching example of autocorrelated errors affecting interpretation of OLS

[Andy Bunn]

HI all, thanks to all those to pointed me towards good environmental data sets for teaching spatial stats in R. We are plugging along on point patterns this week.

This next query might be a bit of stretch but here goes.

This class I'm teaching is made up of master's students who are from a variety of environmental fields (oceanography to toxicology to plant ecology). It's a fun group. A few of them get the gospel of thinking about space in terms of how pattern drives process and some learn to appreciate a spatial perspective because it is just a worthwhile thing in and of itself.

However, a lot of the students just want to make sure that spatial autocorrelation isn't breaking their regressions. Many of them are doing some kind of regression analysis in their thesis work and are worried about spatial autocorrelation violating the regression assumptions (via non iid errors). I have them read (in order):

  1.  Hawkins et al. 2007 (DOI: 10.1111/j.0906-7590.2007.05117.x)
  2.  Hawkins 2012 (DOI: 10.1111/j.1365-2699.2011.02637.x)
  3.  Kuhn & Dormann 2012 (DOI: 10.1111/j.1365-2699.2012.02716.x)

This both ameliorates some of their worries and worries them more. I also show them via simulation where autocorrelation can lead to trouble.   E.g., I have an example where I simulate a SAR process with varying levels of autocorrelation and show them how an OLS model of y~x with spatially autocorrelated residuals  gives an inefficient estimate of beta. (You do need very high levels of autocorrelation to do this I note.)

What would be better would be to show them a worked example where autocorrelation has led to incorrect interpretation of some ecological process. Do any of you know of a case study like this? Something along the lines of "Smith et al thought Y was modeled well by X but when you consider  the spatial structure of the residuals it turns out that their model was interpreted incorrectly."

By the end of the course I want to push more of them over to appreciating spatial analysis for its own sake but do want them to consider the effects of non iid errors on the estimated covariance matrix of the estimates parameters in OLS. (Even if in general OLS is robust - a la Hawkins.)

Sorry for the long email and many thanks, Andy

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