mgcv (version 0.9-6)

s: Defining smooths in GAM formulae

Description

Function used in definition of smooth terms within gam model formulae. The function does not evaluate a (spline) smooth - it exists purely to help set up a model using spline based smooths.

Usage

s(..., k=-1,fx=FALSE,bs="tp",m=0,by=NA)

Arguments

...

a list of variables that are the covariates that this smooth is a function of.

k

the dimension of the basis used to represent the smooth term. The default depends on the number of variables that the smooth is a function of. k should not be less than the dimension of the null space of the penalty for the term (

fx

indicates whether the term is a fixed d.f. regression spline (TRUE) or a penalized regression spline (FALSE).

bs

this can be "cr" for a cubic regression spline or "tp" for a thin plate regression spline. Only thin plate regression splines can be used for multidimensional smooths, so this argument only has an effect for univariat

m

The order of the penalty for this t.p.r.s. term (e.g. 2 for normal cubic spline penalty with 2nd derivatives). O signals autoinitialization, which sets the order to the lowest value satisfying 2m>d+1, where d is the number of covariates: this

by

specifies a covariate by which the whole smooth term is to be multiplied. This is particularly useful for creating models in which a smooth interacts with a factor: in this case the by variable would usually be the dummy variable

Value

• A list with the following items:
• term
  An array of text strings giving the names of the covariates that the term is a function of.
• bs.dim
  The dimension of the basis used to represent the smooth.
• bs.type
  The type of basis. 0 is cubic regression spline. 1 is thin plate regression spline. 0 can only be used for 1-d smooths.
• fixed
  TRUE if the term is to be treated as a pure regression spline (with fixed degrees of freedom); FALSE if it is to be treated as a penalized regression spline
• dim
  The dimension of the smoother - i.e. the number of covariates that it is a function of.
• p.order
  The order of the t.p.r.s. penalty, or 0 for auto-selection of the penalty order.
• by
  is the name of any by variable as text ("NA" for none).
• full.call
  Text for pasting into a string to be converted to a gam formula, which has the values of function options given explicitly - this is useful for constructing a fully expanded gam formula which can be used without needing access to any variables that may have been used to define k, fx, bs or m in the original call. i.e. this is text which when parsed and evaluated generates a call to s() with all the options spelled out explicitly.

url

http://www.stats.gla.ac.uk/~simon/

Details

The function does not evaluate the variable arguments. It will correctly interpret calls like s(x,14|f) (results in pure regression spline smooth of one variable with a 14 knot cubic regression spline basis), s(x,z,20) (a penalized regression spline of 2 covariates using a 20 dimensional t.p.r.s. basis), etc. but this feature is purely for back compatibility reasons, and may not be maintained indefinitely.

See Also

gam

Examples

# example utilising `by' variables
library(mgcv)
set.seed(0)
n<-200;sig2<-4
x1 <- runif(n, 0, 1);x2 <- runif(n, 0, 1);x3 <- runif(n, 0, 1)
fac<-c(rep(1,n/2),rep(2,n/2)) # create factor
fac.1<-rep(0,n)+(fac==1);fac.2<-1-fac.1 # and dummy variables
fac<-as.factor(fac)
f1 <-  exp(2 * x1) - 3.75887
f2 <-  0.2 * x1^11 * (10 * (1 - x1))^6 + 10 * (10 * x1)^3 * (1 - x1)^10 - 1.396
f<-f1*fac.1+f2*fac.2+x2
e <- rnorm(n, 0, sqrt(abs(sig2)))
y <- f + e
# NOTE: smooths will be centered, so need to include fac in model....
b<-gam(y~fac+s(x1,by=fac.1)+s(x1,by=fac.2)+x2) 
plot(b,pages=1)