[R] geometric mean regression

[Michael Grant]

Hi Ted,

Thank you for your informative comments regarding GMR.
   

 
TH:
> This somewhat contentious method 

Contentious...well that says a lot (seriously)!

TH:
> is indeed trivial to implement in R. ...

I implemented it in a simnple brute force
manner--elegance is time--following Helsel and Hirsch.
Get the two slopes to calculate the GMR slope and then
use mean(x) and mean(y) with the new slope to get the
intercept...
 
TH:
> It hardly needs a package!

By itself, no. Your comment is timely given another
help thread currently on the large number of packages
:O). But something like Stats-R-Us and/or the
R-grahpics gallery aimed at useful snippets not worthy
of packages....

MWG:
> > I worked from Helsel's description in his classic
> water
> > resources statistics book. See Chapter 10 here: 
> > 
> > http://water.usgs.gov/pubs/twri/twri4a3/

TH:
> 
> The method goes back a lot further than suggested
> here.

So it seems. After all it has to have been around to
acquire all the different names it goes by. The USGS
book is just good as an online reference. BTW read
'classic' as useful but out of print. I listed the
material because I have found it quite lucid and I
like the emphasis on non-parametric methods. Making
the material available is indeed quite generous of the
authors. I find the book quite thought provoking for
the non-statistics individual. I'm always looking for
insights.

MWG: 
> > Now, if you are after confidence intervals or
> > prediction intervals, I haven't found anything on

TH:
> 
> The uncertainty properties, and indeed the
> interpretation,
> of this method are elusive. 
... 

Now you are getting to the heart of what as been
puzzling me lately. To me the question seemed to be:
does it make sense to even talk about confidence bands
and prediction bands for GMR. It seemed that one can
take a stochastic approach to prediction, i.e., one
can set up simulations and roll the dice over and
over. On one hand it is beyond my knowledge at this
time to ascertain whether or not the the results of
such effort can be couched in the traditional language
of confidence bands and prediction bands about such a
line--neither variable is (in)dependent. Yet if I view
it from the perspective of the minimization of the sum
of the areas of the right triangles (Helsel Fig. 10.8)
determined by each observation and the GMR (LOC), I am
back to a single variable(?)... Oh, well I have not
lost sleep over it, and indeed find your use of the
term 'elusive' reassuring.

> 
> At the other extreme, where there is no correlation,

Being conservative in such matters, little or no
correlation is where I declare defeat and move on to
some other tactic ;O).
> 
> 
> The GMR method seems to be well entrenched in the
> fisheries,
> ... 
> Nevertheless, I'm inclined to the view that the
> linear functional
> relationship is usually the best way to go. When the
> observed
> (x,y) points depart from the "true" points on the
> straight line
> by normally distributed amounts, the MLE of the
> relationship
> is well defined provided the ratio of the
> "departure" variances
> is fixed. Therefore it is possible to examine the
> robustness
> of the estimated relationship with respect to
> variation in the
> assumed value of this ratio. To the extent that this
> is 
> acceptably robust within plausible variation of the
> ratio,
> you have an adequate and reliable perspective.
> Otherwise,
> you have to acknowledge that your information is
> inadquate.
> 
> The danger of adopting a formulaic solution like GMY
> is that
> it tends to conceal inadequacy of information!

Hmmm, more fodder for self study. Thank you very much
for the insights!


Best regards,
Michael Grant