[Rd] odd (erroneous?) results from gls

[Timothy_Handley at nps.gov]

A couple weeks ago I posted a message on this topic to r-help, the response
was that this seemed like odd behavior, and that I ought to post it to one
of the developer lists. I posted to r-sig-mixed-models, but didn't get any
response. So, with good intentions, I decided to try posting once more, but
to this more general list.

The goal is (1) FYI, to make you aware of this issue, in case it is an
error in gls (2) For my information, in case I have made an error, in the
hope that one of you folks might be able to correct me. Thanks in advance
for your time.

The issue is in 2 parts.

(A) I've used gls to fit a model with two fixed effects and a corExp
object. By my count, this fitting process estimates 5 parameters:
(Intercept), l10area, newx, range, and nugget. With 118 total df, there
should be 118 - 5 = 113 residual df. However, the output from summary.gls
reports 115 residual degrees of freedom. Is this an error in summary or
gls, or is there an error in my count?

(B) Summary.gls reports logLik=-273.6. Using my count of 5 estimated
parameters, the AIC should be -2*(-273.6) + 2*5 = 557.2. However,
summary.gls reports an AIC of 559.2. If one works backwards from the
reported AIC of 559.2, it seems that gls believes it has estimated 6
parameters in the fitting process. Again, is this an error in gls, or an
error on my part?

Copied from R terminal:

>
> summary(sppl.i.ex)
Generalized least squares fit by maximum likelihood
  Model: all.all.rch ~ l10area + newx
  Data: gtemp
      AIC      BIC    logLik
  559.167 575.7911 -273.5835

Correlation Structure: Exponential spatial correlation
 Formula: ~x + y | area
 Parameter estimate(s):
     range     nugget
15.4448835  0.3741476

Coefficients:
               Value Std.Error   t-value p-value
(Intercept) 7.621306 0.7648135  9.964921  0.0000
l10area     6.332931 0.5589199 11.330659  0.0000
newx        0.066535 0.0204417  3.254857  0.0015

 Correlation:
        (Intr) l10are
l10area -0.605
newx     0.358 -0.024

Standardized residuals:
       Min         Q1        Med         Q3        Max
-3.0035983 -0.5990432 -0.2226852  0.5113270  2.4444263

Residual standard error: 2.820337
Degrees of freedom: 118 total; 115 residual

Tim Handley
Fire Effects Monitor
Santa Monica Mountains National Recreation Area
401 W. Hillcrest Dr.
Thousand Oaks, CA 91360
805-370-2347