[R] understanding the output from gls

[Timothy_Handley at nps.gov]

I'd like to compare two models which were fitted using gls, however I'm
having trouble interpreting the results of gls. If any of you could offer
me some advice, I'd greatly appreciate it.

Short explanation of models: These two models have the same fixed-effects
structure (two independent, linear effects), and differ only in that the
second model includes a corExp structure for spatial autocorrelation. (more
detailed explanation of the models at end).

Specific questions:

1. The second model estimates two additional parameters in the process of
fitting the corSpatial object - the range and nugget of the spatial
autocorrelation. Based on this, I would expect the second model to have two
fewer residual degrees of freedom. However, the summary function reports
that both models have the same number of residual degrees of freedom.  Why
is this? (Interestingly, the difference in AIC between the two models
reflects this difference in the number of model parameters)

2. In the model summary, what is the meaning of the small correlation
matrix under the heading "Correlation:"? At first, I thought that this was
describing possible correlations among the predictor variables, but then I
saw that it also included the model intercept. What do these correlation
value mean?

##More detailed information
##function calls:
  sppl.i.xx = gls(all.all.rch~l10area+newx, data = gtemp, method="ML")
  sppl.i.ex = gls(all.all.rch~l10area+newx, data = gtemp, method="ML",
              correlation = corExp(c(20,.8), form=~x+y|area, nugget=TRUE))

##model summaries

> summary(sppl.i.xx)
Generalized least squares fit by maximum likelihood
  Model: all.all.rch ~ l10area + newx
  Data: gtemp
       AIC     BIC    logLik
  567.4893 578.572 -279.7446

Coefficients:
               Value Std.Error   t-value p-value
(Intercept) 6.891867 0.3295097 20.915522   0e+00
l10area     6.586182 0.3048870 21.602046   0e+00
newx        0.047901 0.0117281  4.084307   1e-04

 Correlation:
        (Intr) l10are
l10area -0.364
newx     0.577 -0.007

Standardized residuals:
        Min          Q1         Med          Q3         Max
-3.34307266 -0.57949890 -0.07214605  0.64309760  2.66409931

Residual standard error: 2.590313
Degrees of freedom: 118 total; 115 residual

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     6.400442 0.5588160 11.453576  0.0000
newx        0.066535 0.0204417  3.254857  0.0015

 Correlation:
        (Intr) l10are
l10area -0.592
newx     0.358  0.014

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