mgcv (version 1.7-23)

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=NA,by=NA,xt=NULL,id=NULL,sp=NULL)

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

a two letter character string indicating the (penalized) smoothing basis to use. (eg "tp" for thin plate regression spline, "cr" for cubic regression spline). see smooth.terms

m

The order of the penalty for this term (e.g. 2 for normal cubic spline penalty with 2nd derivatives when using default t.p.r.s basis). NA signals autoinitialization. Only some smooth classes use this. The "ps" cl

by

a numeric or factor variable of the same dimension as each covariate. In the numeric vector case the elements multiply the smooth, evaluated at the corresponding covariate values (a `varying coefficient model' results). For the numeric by v

xt

Any extra information required to set up a particular basis. Used e.g. to set large data set handling behaviour for "tp" basis.

id

A label or integer identifying this term in order to link its smoothing parameters to others of the same type. If two or more terms have the same id then they will have the same smoothing paramsters, and, by default,

sp

any supplied smoothing parameters for this term. Must be an array of the same length as the number of penalties for this smooth. Positive or zero elements are taken as fixed smoothing parameters. Negative elements signal auto-initialization. Over-rides v

Value

• A class xx.smooth.spec object, where xx is a basis identifying code given by the bs argument of s. These smooth.spec objects define smooths and are turned into bases and penalties by smooth.construct method functions.

  The returned object contains 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.
• 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).
• label
  A suitable text label for this smooth term.
• xt
  The object passed in as argument xt.
• id
  An identifying label or number for the smooth, linking it to other smooths. Defaults to NULL for no linkage.
• sp
  array of smoothing parameters for the term (negative for auto-estimation). Defaults to NULL.

Details

The function does not evaluate the variable arguments. To use this function to specify use of your own smooths, note the relationships between the inputs and the output object and see the example in smooth.construct.

References

Wood, S.N. (2003) Thin plate regression splines. J.R.Statist.Soc.B 65(1):95-114

Wood S.N. (2006) Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC Press.

http://www.maths.bath.ac.uk/~sw283/

See Also

te, gam, gamm

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
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)+x2) 
plot(b,pages=1)