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xx.smooth.spec during processing of the formula. Each of these objects is
converted to a smooth object using an appropriate smooth.construct function. New smooth classes
can be added by writing a new smooth.construct method function and a corresponding
Predict.matrix method function (see example code below).In practice, smooth.construct is usually called via smooth.construct2 and the wrapper
function smoothCon, in order to handle by variables and
centering constraints (see the smoothCon documentation if
you need to handle these things directly, for a user defined smooth class).
smooth.construct(object,data,knots)
smooth.construct2(object,data,knots)by variable, or "NA".TRUE) any of the margins in the
tensor product should be unpenalized.TRUE if multiple penalties are to be used.TRUE if 1-D marginal smooths are to be re-parameterized in terms of
function values.NULL by default, indicating no linkage.NULL (default),
over-rides sp argument to gam.object, assigned a new class to indicate what type of smooth it is and with at least the
following items added:"offset"
attribute: a vector of length nrow(X) containing any contribution of
the smooth to the model offset term. by variables do not need to be
dealt with here, but if they are then an item by.done must be added to
the object.NULL then
smoothCon will add an identifiability constraint that each term should
sum to zero over the covariate values. Set to a zero row matrix if no
constraints are required. Note that a supplied C is never ignored, even if any
by variables of a smooth imply that no constraint is actually needed.gamm requires it).
Turning off rescaling is useful if the values of the smoothing parameters should be interpretable in a model,
for example because they are inverse variance components.smoothCon will set it to the basis
dimension. smoothCon will reduce this by the number of constraints.S. In this case L is the matrix mapping the vector of underlying log smoothing
parameters to the vector of logs of the smoothing parameters actually multiplying the S[[i]].
L=NULL signifies that there is one smoothing parameter per S[[i]].Predict.matrix methods to make predictions using the basis. See
the Details section for links to the information included for the built in smooth classes. tensor.smooth returned objects will additionally have each element of
the margin list updated in the same way. tensor.smooths also
have a list, XP, containing re-parameterization matrices for any 1-D marginal terms
re-parameterized in terms of function values. This list will have NULL
entries for marginal smooths that are not re-parameterized, and is only long
enough to reach the last re-parameterized marginal in the list.
smooth.construct2"qrc" or "nCons" as these are used internally to provide
constraint free parameterizations.tp.smooth.spec (thin plate regression splines: see tprs);
ts.smooth.spec (thin plate regression splines with shrinkage-to-zero);
cr.smooth.spec (cubic regression splines: see cubic.regression.spline;
cs.smooth.spec (cubic regression splines with shrinkage-to-zero);
cc.smooth.spec (cyclic cubic regression splines);
ps.smooth.spec (Eilers and Marx (1986) style P-splines: see p.spline);
cp.smooth.spec (cyclic P-splines)
ad.smooth.spec (adaptive smooths of 1 or 2 variables: see adaptive.smooth);
tensor.smooth.spec (tensor product smooths).There is an implicit assumption that the basis only depends on the knots and/or the set of unique covariate combinations; i.e. that the basis is the same whether generated from the full set of covariates, or just the unique combinations of covariates.
Wood, S.N. (2006) Low rank scale invariant tensor product smooths for generalized additive mixed models. Biometrics 62(4):1025-1036
The P-spline code given in the example is based on those advocated in:
Ruppert, D., M.P. Wand and R.J. Carroll (2003) Semiparametric Regression. Cambridge University Press.
However if you want p-splines, rather than splines with derivative based penalties, then the built in "ps" class is probably a better bet. It's based on
Eilers, P.H.C. and B.D. Marx (1996) Flexible Smoothing with B-splines and Penalties. Statistical Science, 11(2):89-121
s,get.var, gamm, gam,
Predict.matrix,
smoothCon, PredictMat# adding "p-spline" classes and methods
smooth.construct.tr.smooth.spec<-function(object,data,knots)
## a truncated power spline constructor method function
## object$p.order = null space dimension
{ m <- object$p.order[1]
if (is.na(m)) m <- 2 ## default
if (m<1) stop("silly m supplied")
if (object$bs.dim<0) object$bs.dim <- 10 ## default
nk<-object$bs.dim-m-1 ## number of knots
if (nk<=0) stop("k too small for m")
x <- data[[object$term]] ## the data
x.shift <- mean(x) # shift used to enhance stability
k <- knots[[object$term]] ## will be NULL if none supplied
if (is.null(k)) # space knots through data
{ n<-length(x)
k<-quantile(x[2:(n-1)],seq(0,1,length=nk+2))[2:(nk+1)]
}
if (length(k)!=nk) # right number of knots?
stop(paste("there should be ",nk,"supplied knots"))
x <- x - x.shift # basis stabilizing shift
k <- k - x.shift # knots treated the same!
X<-matrix(0,length(x),object$bs.dim)
for (i in 1:(m+1)) X[,i] <- x^(i-1)
for (i in 1:nk) X[,i+m+1]<-(x-k[i])^m*as.numeric(x>k[i])
object$X<-X # the finished model matrix
if (!object$fixed) # create the penalty matrix
{ object$S[[1]]<-diag(c(rep(0,m+1),rep(1,nk)))
}
object$rank<-nk # penalty rank
object$null.space.dim <- m+1 # dim. of unpenalized space
## store "tr" specific stuff ...
object$knots<-k;object$m<-m;object$x.shift <- x.shift
object$df<-ncol(object$X) # maximum DoF (if unconstrained)
class(object)<-"tr.smooth" # Give object a class
object
}
Predict.matrix.tr.smooth<-function(object,data)
## prediction method function for the `tr' smooth class
{ x <- data[[object$term]]
x <- x - object$x.shift # stabilizing shift
m <- object$m; # spline order (3=cubic)
k<-object$knots # knot locations
nk<-length(k) # number of knots
X<-matrix(0,length(x),object$bs.dim)
for (i in 1:(m+1)) X[,i] <- x^(i-1)
for (i in 1:nk) X[,i+m+1] <- (x-k[i])^m*as.numeric(x>k[i])
X # return the prediction matrix
}
# an example, using the new class....
set.seed(100)
dat <- gamSim(1,n=400,scale=2)
b<-gam(y~s(x0,bs="tr",m=2)+s(x1,bs="ps",m=c(1,3))+
s(x2,bs="tr",m=3)+s(x3,bs="tr",m=2),data=dat)
plot(b,pages=1)
b<-gamm(y~s(x0,bs="tr",m=2)+s(x1,bs="ps",m=c(1,3))+
s(x2,bs="tr",m=3)+s(x3,bs="tr",m=2),data=dat)
plot(b$gam,pages=1)
# another example using tensor products of the new class
dat <- gamSim(2,n=400,scale=.1)$data
b <- gam(y~te(x,z,bs=c("tr","tr"),m=c(2,2)),data=dat)
vis.gam(b)Run the code above in your browser using DataLab