[R] How to automate this model selection algorithm?

[Andrew Crane-Droesch]

I've got a complicated semi-parametric model that I'm fitting with 
mgcv.  I start with a model based on theory.  Its got lots of 
interaction terms.  I want to winnow it down: removing each interaction 
term or un-interacted main effect one by one, checking the AIC, and 
retaining the model that gives me the lowest AIC.  I then want to repeat 
the procedure on the retained model.

Here is a simple example:

     set.seed(42)
     library(mgcv)
     N=220
     fac = ceiling(runif(N)*2)
     a = rnorm(N); b = rnorm(N); c = rnorm(N); d = runif(N); e = rnorm(N);
     y = a^fac + b*e + d/(e+1)

     m1 = gam(y~     as.factor(fac)
     +    s(a)
     +    s(b)
     +    s(c)
     +    s(d)
     +    te(a,b,c)
     +    te(a,d,by=as.factor(fac))
     )

     m2 = gam(y~     as.factor(fac)
     +    s(a)
     +    s(b)
     +    s(c)
     +    s(d)
     +    te(b,c)
     +    te(a,d,by=as.factor(fac))
     )

     m3 = gam(y~     as.factor(fac)
     +    s(a)
     +    s(b)
     +    s(c)
     +    s(d)
     +    te(a,c)
     +    te(a,d,by=as.factor(fac))
     )

     m4 = gam(y~     as.factor(fac)
     +    s(a)
     +    s(b)
     +    s(c)
     +    s(d)
     +    te(a,b)
     +    te(a,d,by=as.factor(fac))
     )

     m5 = gam(y~     as.factor(fac)
     +    s(a)
     +    s(b)
     +    s(c)
     +    s(d)
     +    te(a,b,c)
     +    te(d,by=as.factor(fac))
     )

     m6 = gam(y~     as.factor(fac)
     +    s(a)
     +    s(b)
     +    s(c)
     +    s(d)
     +    te(a,b,c)
     +    te(a,by=as.factor(fac))
     )

     m7 = gam(y~     as.factor(fac)
     +    s(a)
     +    s(b)
     +    s(c)
     +    s(d)
     +    te(a,b,c)
     +    te(a,d)
     )

     selection = AIC(m1,m2,m3,m4,m5,m6,m7)
     selection

df      AIC

m1 14.53435 1626.611

m2 12.52501 1622.635

m3 12.54566 1622.615

m4 12.52652 1622.633

m5 13.14108 1620.759

m6 10.99684 1621.156

m7 10.98136 1622.229

m5 is the best

     m5 = gam(y~     as.factor(fac)
     +    s(a)
     +    s(b)
     +    s(c)
     +    s(d)
     +    te(a,b,c)
     +    te(d,by=as.factor(fac))
     )

     m5.1 = gam(y~     as.factor(fac)
     +    s(a)
     +    s(b)
     +    s(c)
     +    s(d)
     +    te(b,c)
     +    te(d,by=as.factor(fac))
     )

     m5.2 = gam(y~     as.factor(fac)
     +    s(a)
     +    s(b)
     +    s(c)
     +    s(d)
     +    te(a,c)
     +    te(d,by=as.factor(fac))
     )
     m5.3 = gam(y~     as.factor(fac)
     +    s(a)
     +    s(b)
     +    s(c)
     +    s(d)
     +    te(a,b)
     +    te(d,by=as.factor(fac))
     )

     m5.4 = gam(y~     as.factor(fac)
     +    s(a)
     +    s(b)
     +    s(c)
     +    s(d)
     +    te(a,b,c)
     #+    te(d,by=as.factor(fac))
     )

     selection.2 = AIC(m5,m5.1,m5.2,m5.3,m5.4)
     selection.2

df      AIC

m5   13.363029 1621.183

m5.1  9.671656 1617.641

m5.2  9.730047 1617.549

m5.3  9.706424 1617.569

m5.4  9.857504 1620.028

5.2 is the best

...and so on.  I'd next try out each interaction term or un-interacted 
main effect in m5.2.  Question is how I can automate this?  To start 
with a model (m1, in my case), and have R give me the best model after 
running this algorithm to the point where there are no longer any 
"better" models according to this algorithm?

Right now I can do it manually, but as I add data over time, model 
selection may change.

Note the mgcv's "select=TRUE" functionality doesn't quite work for me 
(at least not directly), because I want to see if single parts of 
three-way interactions can/should be removed.

Thanks in advance for any tips, and apologies for cross-posting (on 
stack overflow).

Best,
Andrew