[R-sig-Geo] GLS/OLS

Edzer Pebesma edzer.pebesma at uni-muenster.de
Thu Aug 16 22:13:48 CEST 2012



On 08/16/2012 02:29 PM, M.Kuntz at stud.uni-heidelberg.de wrote:
> 
> Dear List members,
> 
> after reading several old mail from R-sig-geo and checking the gstat
> manual there is still sth. confusion about the way how gstat calculates
> the Regressions.
> On the on hand some mails, as the the following one, tell that GLS is
> used to estimate the Regressioncoefficients and the error:
> http://mailman.geo.uu.nl/pipermail/gstat-info/2006q3/000091.html
> 
>> I am not quite clear how gls works.  Is this an iterative approach, some
>> thing like
>> 1) Use OLS to estimate the betas (globally)
>> 2) Calcualte the residuals
>> 3) Calculate and model the variogram
>> 4) Get the covariance matrix
>> 5) Use GLS to calculate the betas
>> 6) Go back to (2) and repeat until convergence.
>> The resulting betas and variogram are then used for kriging, as
>> described above.  Is this right?
>>
>>
> No, the order gstat does in a single pass is 4, 5, 2, 3: you feed it
> with a variogram, this variogram is used to obtain gls residuals instead
> of ols. After 3, you could repeat this, but gstat has not an automated
> looping mechanism for this (the interactive menu can be used for it, but
> requires the user to do the iterations).
> 
> So does the gstat manual as it tells that there is the possibility of
> calculating only the regressioncoefficients by using
>> predict( ..., BLUE=TRUE), which implicates that GLS is used.
> 
> On the other hand there exists the command
>> gstat( ..., set = list(gls = 1) )
> and the manual reads as follows:
> 
> "By default, the residuals gstat uses are ordinary least squares residuals
> (i.e. regular regression residuals), meaning that for the sake of
> estimating
> the trend, observations are considered independent. To honour a dependence
> structure present, generalised least squares residuals can be calculated
> instead.
> For this, a variogram model to define the covariance structure is
> needed. In
> the following example..."
> 
> which implicates that by default OLS is used.
> 
> So I am asking: What exactly occurs, when I use the predict.gstat command?
> Is it possibly that, by default, the Trend is fitted by OLS and then the
> variogram if fitted by GLS? But why is there this BLUE=TRUE option for
> the predict.gstat command?
> 

predict.gstat will always use the variogram model passed, so uses GLS
unless a pure nugget model is passed (in which case GLS and OLS are
identical).

The example in ?variogram shows how you can get a variogram from GLS
residuals, by default OLS residuals are used HERE (and when dX is not set).

BLUE=TRUE is used in predict.gstat to get the trend component ONLY at
prediction locations, instead of the trend+predicted residual which what
we call kriging.

If all this is confusing from the manuals, please let me know what
exactly confused you.

> 
> 
> Any help would be appreciated.
> 
> Cheers!  Michael
> 
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-- 
Edzer Pebesma
Institute for Geoinformatics (ifgi), University of Münster
Weseler Straße 253, 48151 Münster, Germany. Phone: +49 251
8333081, Fax: +49 251 8339763  http://ifgi.uni-muenster.de
http://www.52north.org/geostatistics      e.pebesma at wwu.de



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