Re: [R] understanding the output from gls
Kingsford,
Thanks for the information. As you suggest, if I don't hear from anyone
else about the degrees of freedom issue in a couple days, I'll try r-devel.
Also, while I appreciate your explanation of the correlation matrix
produced by summary.gls, I'm afriad I don't have the statistical background
to fully understand it. If it wouldn't impose too much on your time, could
you suggest a more intuitive way to interpret these numbers, or perhaps a
reference with a more intuitive explanation?
To me, the idea that fixed effects estimates could be correlated just
sounds odd. I understand that the effects themselves could be correlated.
While I have good biological reasons for thinking that my two fixed effects
are independent, the data may prove me wrong. However, the fixed effects
estimates are each just a single number for the data/model as a whole. How
can one pair of two single numbers be correlated?
Tim Handley
Fire Effects Monitor
Santa Monica Mountains National Recreation Area
401 W. Hillcrest Dr.
Thousand Oaks, CA 91360
805-370-2347
Kingsford Jones
kingsfordjo...@g
mail.com To
timothy_hand...@nps.gov
09/01/2009 05:53 cc
PMR-help@r-project.org
Subject
Re: [R] understanding the output
from gls
Hi Tim,
On Tue, Sep 1, 2009 at 2:00 PM, timothy_hand...@nps.gov wrote:
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),
Known to be independent?
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)
That's a good question. It does seem degrees of freedom would be
spent in estimating the spatial parameters.
The reason the functions using logLik get the number of parameters
right is because logLik.gls includes:
attr(val, df) - p + length(coef(object[[modelStruct]])) + 1
where modelStruct holds the estimated parameters that structure
residual variance and correlation, and I believe p is the number of
columns in the design matrix, but I couldn't easily follow the code
within gls that produces it.
If nobody offers an explanation for the current result from
print.summary.gls you could ask on r-devel if the results are
intended.
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?
The GLS covariance of estimated fixed effects (including the
intercept) is (X' \hat{\Sigma}^-1 X)^-1, where X is the model matrix
and \Sigma is the response/error covariance matrix. This will
generally have non-zero off-diagonals, implying the fixed effects
estimates are correlated. The values you're inquiring about are the
scaled estimates of those off-diagonals.
hth,
Kingsford Jones
##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
Re: [R] understanding the output from gls
On Wed, Sep 2, 2009 at 2:39 PM, timothy_hand...@nps.gov wrote:
Kingsford,
Thanks for the information. As you suggest, if I don't hear from anyone
else about the degrees of freedom issue in a couple days, I'll try r-devel.
Determining denominator degrees of freedom for F tests in mixed models
is an area of current research (and some contention) and it may be
that the same holds true for df in a linear model w/ estimated
parameters structuring the error covariance. So, these may be some
deep waters that nobody is eager to wade intoor maybe there's a
simple explanation...
Also, while I appreciate your explanation of the correlation matrix
produced by summary.gls, I'm afriad I don't have the statistical background
to fully understand it. If it wouldn't impose too much on your time, could
you suggest a more intuitive way to interpret these numbers, or perhaps a
reference with a more intuitive explanation?
To me, the idea that fixed effects estimates could be correlated just
sounds odd. I understand that the effects themselves could be correlated.
While I have good biological reasons for thinking that my two fixed effects
are independent, the data may prove me wrong. However, the fixed effects
estimates are each just a single number for the data/model as a whole. How
can one pair of two single numbers be correlated?
Well the issue is that you're assuming a model. Here's a simple idea
that may help you intuition:
Visualize a scatterplot and place a point on that plot that marks
(mean x, mean y). The way the math works out, a regression line fit
to the data must go through that point. Now think about adjusting the
intercept of that line, while keeping it going through the (mean x,
mean y) point -- clearly the slope will change too. So, x and y are
not independent.
The reason the covariance matrix of the fixed effects coefficients is
usually of interest is for inference. For example a joint confidence
region for the slope and intercept would be an ellipse with elongation
determined by the covariance.
hth,
Kingsford
Tim Handley
Fire Effects Monitor
Santa Monica Mountains National Recreation Area
401 W. Hillcrest Dr.
Thousand Oaks, CA 91360
805-370-2347
Kingsford Jones
kingsfordjo...@g
mail.com To
timothy_hand...@nps.gov
09/01/2009 05:53 cc
PM r-h...@r-project.org
Subject
Re: [R] understanding the output
from gls
Hi Tim,
On Tue, Sep 1, 2009 at 2:00 PM, timothy_hand...@nps.gov wrote:
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),
Known to be independent?
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)
That's a good question. It does seem degrees of freedom would be
spent in estimating the spatial parameters.
The reason the functions using logLik get the number of parameters
right is because logLik.gls includes:
attr(val, df) - p + length(coef(object[[modelStruct]])) + 1
where modelStruct holds the estimated parameters that structure
residual variance and correlation, and I believe p is the number of
columns in the design matrix, but I couldn't easily follow the code
within gls that produces it.
If nobody offers an explanation for the current result from
print.summary.gls you could ask on r-devel if the results are
intended.
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?
The GLS covariance of estimated fixed effects (including the
intercept) is (X' \hat{\Sigma}^-1 X)^-1, where X is the model matrix
and \Sigma is the response/error
Re: [R] understanding the output from gls
Hi Tim,
On Tue, Sep 1, 2009 at 2:00 PM, timothy_hand...@nps.gov wrote:
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),
Known to be independent?
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)
That's a good question. It does seem degrees of freedom would be
spent in estimating the spatial parameters.
The reason the functions using logLik get the number of parameters
right is because logLik.gls includes:
attr(val, df) - p + length(coef(object[[modelStruct]])) + 1
where modelStruct holds the estimated parameters that structure
residual variance and correlation, and I believe p is the number of
columns in the design matrix, but I couldn't easily follow the code
within gls that produces it.
If nobody offers an explanation for the current result from
print.summary.gls you could ask on r-devel if the results are
intended.
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?
The GLS covariance of estimated fixed effects (including the
intercept) is (X' \hat{\Sigma}^-1 X)^-1, where X is the model matrix
and \Sigma is the response/error covariance matrix. This will
generally have non-zero off-diagonals, implying the fixed effects
estimates are correlated. The values you're inquiring about are the
scaled estimates of those off-diagonals.
hth,
Kingsford Jones
##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.
l10area 6.400442 0.5588160 11.453576 0.
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 2.263
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
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__
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
