gam.side {mgcv} | R Documentation

## Identifiability side conditions for a GAM

### Description

GAM formulae with repeated variables only correspond to identifiable models given some side conditions. This routine works out appropriate side conditions, based on zeroing redundant parameters. It is called from `gam.setup` and is not intended to be called by users.

The method identifies nested and repeated variables by their names, but evaluates what constraints to impose, numerically. Constraints are always applied to smooths of more variables in preference to smooths of fewer variables. The numerical approach allows appropriate constraints to be applied to models constructed using any smooths, including user defined smooths.

### Usage

    gam.side(sm,tol=.Machine$double.eps^.5)

### Arguments

`sm` | A list of smooth objects as returned by `smooth.construct`.
`tol` | The tolernce to use when assessing linear dependence of smooths.

### Details

Models such as `y~s(x)+s(z)+s(x,z)` can be estimated by `gam`, but require identifiability constraints to be applied, to make them identifiable. This routine does this, effectively setting redundant parameters to zero. When the redundancy is between smooths of lower and higher numbers of variables, the constraint is always applied to the smooth of the higher number of variables.

Dependent smooths are identified symbolically, but which constraints are needed to ensure identifiability of these smooths is determined numerically, using `fixDependence`. This makes the routine rather general, and not dependent on any particular basis.

### Value

A list of smooths, with model matrices and penalty matrices adjusted to automatically impose the required constraints. Any smooth that has been modified will have an attribute `"del.index"`, listing the columns of its model matrix that were deleted. This index is used in the creation of prediction matrices for the term.

### Author(s)

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

### Examples

    set.seed(0)
    n<-400
    sig2<-4
    x0 <- runif(n, 0, 1)
    x1 <- runif(n, 0, 1)
    x2 <- runif(n, 0, 1)
    pi <- asin(1) * 2
    f <- 2 * sin(pi * x0)
    f <- f + exp(2 * x1) - 3.75887
    f <- f + 0.2 * x2^11 * (10 * (1 - x2))^6 + 10 * (10 * x2)^3 * (1 - x2)^10 - 1.396
    e <- rnorm(n, 0, sqrt(abs(sig2)))
    y <- f + e
    b<-gam(y~s(x0)+s(x1)+s(x0,x1)+s(x2))
    plot(b,pages=1)
    test1<-function(x,z,sx=0.3,sz=0.4)
    { (pi**sx*sz)*(1.2*exp(-(x-0.2)^2/sx^2-(z-0.3)^2/sz^2)+
      0.8*exp(-(x-0.7)^2/sx^2-(z-0.8)^2/sz^2))
    }
    n<-500
    old.par<-par(mfrow=c(2,2))
    x<-runif(n);z<-runif(n);
    y<-test1(x,z)+rnorm(n)*0.1
    ## a fully nested tensor product example
    b<-gam(y~s(x,bs="cr",k=6)+s(z,bs="cr",k=6)+te(x,z,k=6))
    plot(b)
    par(old.par)
    rm(list=c("f","x0","x1","x2","x","z","y","b","test1","n","sig2","pi","e"))

[Package mgcv version 1.3-17 Index]