[R] which coefficients for a gam(mgcv) model equation?

[Gavin Simpson]

On Thu, 2010-03-04 at 14:49 -0800, doon75 wrote:
> Dear users,
> I am trying to show the equation (including coefficients from the model
> estimates) for a gam model but do not understand how to.
> Slide 7 from one of the authors presentations (gam-theory.pdf  URL: 
> http://people.bath.ac.uk/sw283/mgcv/) shows a general equation
> log{E(yi )} = α+ ßxi + f (zi ) .

That would be the model for the Gamma GAM.

> What I would like to do is put my model coefficients and present the
> equation used. I am an ecologist not a statistician - and have no access to
> statistical advice.
> How would I use values from the model below to complete the equation: 
> log{E(yi )} = α+ ßxi + f (zi )?
> Many thanks,
> Darren
> 
> ## from the help
> library(mgcv)
> set.seed(0) ## simulate some data...
> dat <- gamSim(1,n=400,dist="normal",scale=2)
> b<-gam(y~s(x0)+s(x1)+s(x2)+s(x3),data=dat)
> summary(b)

coef(b)

will give you the coefficients for the smooth terms + the intercept for
that model. ?gamObject describes thus a little.

The coefficients for the smooth/spline terms here are of length 9 each,
and each set of 9 coefficients pertains to an f(), so the model in the R
code you gave would be something like

E(y_i) ~ alpha + f_1(x0_i) + f_2(x1_i) + f_3(x2_i) +f_4(x3_i) 

or

E(y_i) = alpha + f_1(x0_i) + f_2(x1_i) + f_3(x2_i) +f_4(x3_i) + e, where
e ~ N(0, sigma)

The first number returned by coef(b) is the intercept term, the alpha
above. The next 9 numbers are the coefficients for the spline (f_1)
fitted to the variable x0, and so on. These coefficients relate to the
set of basis functions used to represent the spline for each covariate
(x0, x1 etc).

Depending on why you want to write out the equation, you may not need
the detail provide at the level of the coefficients. Are the equations
above sufficient for your needs? I'm an ecologist too and rarely do I
need to think about the models I am working with at the level of the
coefficients for the basis functions, but your needs may be different.
If so, perhaps you could provide more details on why you want the
equation for the model?

HTH

G
> 
>  I have tried searching help forum with "gam equation" I was not able to
> find an answer from the 18 threads returned.
> Also tried looking at "?predict.gam" and simply "predict.gam" however my
> understanding of R is not sufficient to understand the details to be able to
> answer my question.
> I checked Simon Woods excellent presentations
> (http://www.maths.bath.ac.uk/~sw283/) however if the answer is there I am
> too stupid to see it. In truth the content assumes a level of basic
> understanding that I don't have. Unfortunately I do not have access to the
> book ( Wood S.N. (2006) Generalized Additive Models: An Introduction with R.
> Chapman and Hall/CRC Press.) or finances necessary to get it.
> Any help would be much appreciated,
> 
> R version 2.10.1 (2009-12-14)
> i386-pc-mingw32
> 
> locale:
> [1] LC_COLLATE=English_United Kingdom.1252  LC_CTYPE=English_United
> Kingdom.1252  
> [3] LC_MONETARY=English_United Kingdom.1252 LC_NUMERIC=C                          
> [5] LC_TIME=English_United Kingdom.1252   
> 
> attached base packages:
> [1] stats     graphics  grDevices utils     datasets  methods   base    
> 
> other attached packages:
> [1] mgcv_1.6-1
> 
> loaded via a namespace (and not attached):
> [1] grid_2.10.1        lattice_0.17-26    Matrix_0.999375-33 nlme_3.1-96      
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