Stepwise model builder for GAM

Builds a GAM model in a step-wise fashion. For each "term" there is an ordered list of alternatives, and the function traverses these in a greedy fashion. Note: this is NOT a method for step, which used to be a generic, so must be invoked with the full name.

Usage

step.Gam(
  object,
  scope,
  scale,
  direction = c("both", "backward", "forward"),
  trace = TRUE,
  keep = NULL,
  steps = 1000,
  parallel = FALSE,
  ...
)

Arguments

object

An object of class Gam or any of it's inheritants.

scope

defines the range of models examined in the step-wise search. It is a list of formulas, with each formula corresponding to a term in the model. Each of these formulas specifies a "regimen" of candidate forms in which the particular term may enter the model. For example, a term formula might be ~1+ Income + log(Income) + s(Income). This means that Income could either appear not at all, linearly, linearly in its logarithm, or as a smooth function estimated nonparametrically. A 1 in the formula allows the additional option of leaving the term out of the model entirely. Every term in the model is described by such a term formula, and the final model is built up by selecting a component from each formula.

As an alternative more convenient for big models, each list can have instead of a formula a character vector corresponding to the candidates for that term. Thus we could have c("1","x","s(x,df=5") rather than ~1+x+s(x,df=5).

The supplied model object is used as the starting model, and hence there is the requirement that one term from each of the term formulas be present in formula(object). This also implies that any terms in formula(object) not contained in any of the term formulas will be forced to be present in every model considered. The function gam.scope is helpful for generating the scope argument for a large model.

scale

an optional argument used in the definition of the AIC statistic used to evaluate models for selection. By default, the scaled Chi-squared statistic for the initial model is used, but if forward selection is to be performed, this is not necessarily a sound choice.

direction

The mode of step-wise search, can be one of "both", "backward", or "forward", with a default of "both". If scope is missing, the default for direction is "both".

trace

If TRUE (the default), information is printed during the running of step.Gam(). This is an encouraging choice in general, since step.Gam() can take some time to compute either for large models or when called with an an extensive scope= argument. A simple one line model summary is printed for each model selected. This argument can also be given as the binary 0 or 1. A value trace=2 gives a more verbose trace.

keep

A filter function whose input is a fitted Gam object, and anything else passed via ..., and whose output is arbitrary. Typically keep() will select a subset of the components of the object and return them. The default is not to keep anything.

steps

The maximum number of steps to be considered. The default is 1000 (essentially as many as required). It is typically used to stop the process early.

parallel

If TRUE, use parallel foreach to fit each trial run. Must register parallel before hand, such as doMC or others. See the example below.

...

Additional arguments to be passed on to keep

Value

The step-wise-selected model is returned, with up to two additional components. There is an "anova" component corresponding to the steps taken in the search, as well as a "keep" component if the keep= argument was supplied in the call.

We describe the most general setup, when direction = "both". At any stage there is a current model comprising a single term from each of the term formulas supplied in the scope= argument. A series of models is fitted, each corrresponding to a formula obtained by moving each of the terms one step up or down in its regimen, relative to the formula of the current model. If the current value for any term is at either of the extreme ends of its regimen, only one rather than two steps can be considered. So if there are p term formulas, at most 2*p - 1 models are considered. A record is kept of all the models ever visited (hence the -1 above), to avoid repetition. Once each of these models has been fit, the "best" model in terms of the AIC statistic is selected and defines the step. The entire process is repeated until either the maximum number of steps has been used, or until the AIC criterion can not be decreased by any of the eligible steps.

References

Hastie, T. J. (1992) Generalized additive models. Chapter 7 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

Hastie, T. and Tibshirani, R. (1990) Generalized Additive Models. London: Chapman and Hall.

Author

Written by Trevor Hastie, following closely the design in the "Generalized Additive Models" chapter (Hastie, 1992) in Chambers and Hastie (1992).

Examples


data(gam.data)
Gam.object <- gam(y~x+z, data=gam.data)
step.object <-step.Gam(Gam.object, scope=list("x"=~1+x+s(x,4)+s(x,6)+s(x,12),"z"=~1+z+s(z,4)))
#> Start:  y ~ x + z; AIC= 127.7316 
#> Step:1 y ~ s(x, 4) + z ; AIC= 44.0543 
#> Step:2 y ~ s(x, 4) ; AIC= 43.1799 
#> Step:3 y ~ s(x, 6) ; AIC= 42.6681 
if (FALSE) { # \dontrun{
# Parallel
require(doMC)
registerDoMC(cores=2)
step.Gam(Gam.object, scope=list("x"=~1+x+s(x,4)+s(x,6)+s(x,12),"z"=~1+z+s(z,4)),parallel=TRUE)
} # }