R/S-Plus equivalent to Genstat "predict": predictions over "averages" of covariates

Hi all

I'm doing some things with a colleague comparing different
sorts of models.  My colleague has fitted a number of glms in
Genstat (which I have never used), while the glm I have
been using is only available for R.

He has a spreadsheet of fitted means from each of his models
obtained from using the Genstat "predict" function.  For
example, suppose we fit the model of the type
    glm.out <- glm( y ~ factor(F1) + factor(F2) + X1 + poly(X2,2) +
       poly(X3,2), family=...)

Then he produces a table like this (made up, but similar):

F1(level1)	12.2
F1(level2)	14.2
F1(level3)	15.3
F2(level1)	10.3
F2(level2)	9.1
X1=0		10.2
X1=0.5		10.4
X1=1 		10.4
X1=1.5		10.5
X1=2		10.9
X1=2.5		11.9
X1=3		11.8
X2=0		12.0
X2=0.5		12.2
X2=1 		12.5
X2=1.5		12.9	
X2=2		13.0
X2=2.5		13.1
X2=3		13.5

Each of the numbers are a predicted mean.  So when X1=0, on average
we predict an outcome of 10.2.

To obtain these figures in Genstat, he uses the Genstat "predict"
function.  When I asked for an explanation of how it was done (ie to
make the "predictions", what values of the other covariates were used) I
was told:

So, for a one-dimensional table of fitted means for any factor (or
variate), all other variates are set to their average values; and the
factor constants (including the first, at zero) are given a weighted
average depending on their respective numbers of observations.

So for quantitative variables (such as pH), one uses the mean pH in the
data set when making the predictions.  Reasonable anmd easy.

But for categorical variables (like Month), he implies we use a weighted
average of the fitted coefficients for all the months, depending on the
proportion of times those factor levels appear in the data.

(I hope I explained that OK...)

Is there an equivalent way in R or S-Plus of doing this?  I have to do
it for a number of sites and species, so an automated way would be
useful.  I have tried searching to no avail (but may not be searching
on the correct terms), and tried hard-coding something myself
as yet unsuccessfully:  The  poly  terms and the use of the weighted
averaging over the factor levels are proving a bit too much for my
limited skills.

Any assistance appreciated.  (Any clarification of what I mean can be
provided if I have not been clear.)

Thanks, as always.

P.

 > version

          _
platform i386-pc-linux-gnu
arch     i386
os       linux-gnu
system   i386, linux-gnu
status
major    2
minor    1.0
year     2005
month    04
day      18
language R

 >

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch 
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Peter Dunn
Sent: Wednesday, October 05, 2005 9:06 PM
To: R-help mailing list
Subject: [R] R/S-Plus equivalent to Genstat "predict": 
predictions over "averages" of covariates

Hi all

I'm doing some things with a colleague comparing different 
sorts of models.  My colleague has fitted a number of glms in 
Genstat (which I have never used), while the glm I have been 
using is only available for R.

He has a spreadsheet of fitted means from each of his models 
obtained from using the Genstat "predict" function.  For 
example, suppose we fit the model of the type
    glm.out <- glm( y ~ factor(F1) + factor(F2) + X1 + poly(X2,2) +
       poly(X3,2), family=...)

Then he produces a table like this (made up, but similar):

F1(level1)	12.2
F1(level2)	14.2
F1(level3)	15.3
F2(level1)	10.3
F2(level2)	9.1
X1=0		10.2
X1=0.5		10.4
X1=1 		10.4
X1=1.5		10.5
X1=2		10.9
X1=2.5		11.9
X1=3		11.8
X2=0		12.0
X2=0.5		12.2
X2=1 		12.5
X2=1.5		12.9	
X2=2		13.0
X2=2.5		13.1
X2=3		13.5

Each of the numbers are a predicted mean.  So when X1=0, on 
average we predict an outcome of 10.2.

To obtain these figures in Genstat, he uses the Genstat "predict"
function.  When I asked for an explanation of how it was done 
(ie to make the "predictions", what values of the other 
covariates were used) I was told:

So, for a one-dimensional table of fitted means for any factor (or 
variate), all other variates are set to their average 

values; and the 

factor constants (including the first, at zero) are given a 

weighted 

average depending on their respective numbers of observations.

So for quantitative variables (such as pH), one uses the mean 
pH in the data set when making the predictions.  Reasonable anmd easy.

But for categorical variables (like Month), he implies we use 
a weighted average of the fitted coefficients for all the 
months, depending on the proportion of times those factor 
levels appear in the data.

(I hope I explained that OK...)

Is there an equivalent way in R or S-Plus of doing this?  I 
have to do it for a number of sites and species, so an 
automated way would be useful.  I have tried searching to no 
avail (but may not be searching on the correct terms), and 
tried hard-coding something myself as yet unsuccessfully:  
The  poly  terms and the use of the weighted averaging over 
the factor levels are proving a bit too much for my limited skills.

Any assistance appreciated.  (Any clarification of what I 
mean can be provided if I have not been clear.)

Thanks, as always.

P.

 > version

          _
platform i386-pc-linux-gnu
arch     i386
os       linux-gnu
system   i386, linux-gnu
status
major    2
minor    1.0
year     2005
month    04
day      18
language R

 >

--
Dr Peter Dunn  |  Senior Lecturer in Statistics Faculty of 
Sciences, University of Southern Queensland
   Web:    http://www.sci.usq.edu.au/staff/dunn
   Email:  dunn <at> usq.edu.au
CRICOS:  QLD 00244B |  NSW 02225M |  VIC 02387D |  WA 02521C