s {mgcv} | R Documentation

## 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 (see `null.space.dimension`), but will be reset if it is. See `choose.k` for further information.
`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, `"cs"` for a cubic regression spline with shrinkage, `"cc"` for a cyclic (periodic) spline, `"tp"` for a thin plate regression spline, `"ts"` for a thin plate regression spline with shrinkage or a user defined character string for other user defined smooth classes. Of the built in alternatives, only thin plate regression splines can be used for multidimensional smooths. Note that the `"cr"` and `"cc"` bases are faster to set up than the `"tp"` basis, particularly on large data sets (although the `knots` argument to `gam` can be used to get round this).

`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 choise ensures visual smoothness. In addition, m must satisfy the technical restriction 2m>d, otherwise it will be autoinitialized.
`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 coding one level of the factor. See the examples below. This is the means by which `variable coefficient models' can be specified.

### 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`.

### 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).

`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.

`label` | A suitable text label for this smooth term.

### Author(s)

Simon N. Wood simon.wood@r-project.org

### References

Wood, S.N. (2000) Modelling and Smoothing Parameter Estimation with Multiple Quadratic Penalties. J.R.Statist.Soc.B 62(2):413-428

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

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.1)+s(x1,by=fac.2)+x2)
    plot(b,pages=1)

[Package mgcv version 1.3-23 Index]