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

Tim Meehan tmeeha at gmail.com
Mon May 2 22:01:26 CEST 2016

Hi Andy,

You can use the following for an example:



On Mon, May 2, 2016 at 1:52 PM, Andy Bunn <Andy.Bunn at wwu.edu> wrote:

> 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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