predict.gam {mgcv}  R Documentation 
Takes a fitted gam
object produced by gam()
and produces predictions given a new set of values for the model covariates
or the original values used for the model fit. Predictions can be accompanied
by standard errors, based on the posterior distribution of the model
coefficients. The routine can optionally return the matrix by which the model
coefficients must be premultiplied in order to yield the values of the linear predictor at
the supplied covariate values: this is useful for obtaining credible regions
for quantities derived from the model, and for lookup table prediction outside
R
(see example code below).
## S3 method for class 'gam': predict(object,newdata,type="link",se.fit=FALSE,terms=NULL, block.size=1000,newdata.guaranteed=FALSE,na.action=na.pass,...)
object 
a fitted gam object as produced by gam() .

newdata 
A data frame containing the values of the model covariates at which predictions
are required. If this is not provided then predictions corresponding to the
original data are returned. If newdata is provided then
it should contain all the variables needed for prediction: a
warning is generated if not. 
type 
When this has the value "link" (default) the linear predictor (possibly with
associated standard errors) is returned. When type="terms" each component of the
linear predictor is returned seperately (possibly with standard errors): this includes
parametric model components, followed by each smooth component, but excludes
any offset and any intercept. When type="response" predictions
on the scale of the response are returned (possibly with approximate
standard errors). When type="lpmatrix" then a matrix is returned
which yields the values of the linear predictor (minus any offset) when
postmultiplied by the
parameter vector (in this case se.fit is ignored). The latter
option is most useful for getting variance estimates for quantities derived from
the model: for example integrated quantities, or derivatives of smooths. A
linear predictor matrix can also be used to implement approximate prediction
outside R (see example code, below). 
se.fit 
when this is TRUE (not default) standard error estimates are returned for each prediction. 
terms 
if type=="terms" then only results for the terms given in this array
will be returned. 
block.size 
maximum number of predictions to process per call to underlying code: larger is quicker, but more memory intensive. Set to < 1 to use total number of predictions as this. 
newdata.guaranteed 
Set to TRUE to turn off all checking of
newdata except for sanity of factor levels: this can speed things up
for large prediction tasks, but newdata must be complete, with no
NA values for predictors required in the model. 
na.action 
what to do about NA values in newdata . With the
default na.pass , any row of newdata containing NA values
for required predictors, gives rise to NA predictions (even if the term concerned has no
NA predictors). na.exclude or na.omit result in the
dropping of newdata rows, if they contain any NA values for
required predictors. If newdata is missing then NA handling is
determined from object$na.action . 
... 
other arguments. 
The standard errors produced by predict.gam
are based on the
Bayesian posterior covariance matrix of the parameters Vp
in the fitted
gam object.
To facilitate plotting with termplot
, if object
possesses
an attribute "para.only"
and type=="terms"
then only parametric
terms of order 1 are returned (i.e. those that termplot
can handle).
Note that, in common with other prediction functions, any offset supplied to
gam
as an argument is always ignored when predicting, unlike
offsets specified in the gam model formula.
See the examples for how to use the lpmatrix
for obtaining credible
regions for quantities derived from the model.
If type=="lpmatrix"
then a matrix is returned which will
give a vector of linear predictor values (minus any offest) at the supplied covariate
values, when applied to the model coefficient vector.
Otherwise, if se.fit
is TRUE
then a 2 item list is returned with items (both arrays) fit
and se.fit
containing predictions and associated standard error estimates, otherwise an
array of predictions is returned. The dimensions of the returned arrays depends on whether
type
is "terms"
or not: if it is then the array is 2 dimensional with each
term in the linear predictor separate, otherwise the array is 1 dimensional and contains the
linear predictor/predicted values (or corresponding s.e.s). The linear predictor returned termwise will
not include the offset or the intercept.
newdata
can be a data frame, list or model.frame: if it's a model frame
then all variables must be supplied.
Note that the behaviour of this function is not identical to
predict.gam()
in Splus.
type=="terms"
does not exactly match what predict.lm
does for
parametric model components.
Simon N. Wood simon.wood@rproject.org
The design is inspired by the S function of the same name described in Chambers and Hastie (1993) (but is not a clone).
Chambers and Hastie (1993) Statistical Models in S. Chapman & Hall.
Gu and Wahba (1991) Minimizing GCV/GML scores with multiple smoothing parameters via the Newton method. SIAM J. Sci. Statist. Comput. 12:383398
Wood, S.N. (2000) Modelling and Smoothing Parameter Estimation with Multiple Quadratic Penalties. J.R.Statist.Soc.B 62(2):413428
Wood, S.N. (2003) Thin plate regression splines. J.R.Statist.Soc.B 65(1):95114
Wood, S.N. (2004) Stable and efficient multiple smoothing parameter estimation for generalized additive models. J. Amer. Statist. Ass. 99:637686
http://www.maths.bath.ac.uk/~sw283/
library(mgcv) n<200 sig < 2 x0 < runif(n, 0, 1) x1 < runif(n, 0, 1) x2 < runif(n, 0, 1) x3 < runif(n, 0, 1) y < 2 * sin(pi * x0) y < y + exp(2 * x1) y < y + 0.2 * x2^11 * (10 * (1  x2))^6 + 10 * (10 * x2)^3 * (1  x2)^10 y < y + x3 e < rnorm(n, 0, sig) y < y + e b<gam(y~s(x0)+s(I(x1^2))+s(x2)+offset(x3)) rm(y,x0,x1,x2,x3) newd < data.frame(x0=(0:30)/30,x1=(0:30)/30,x2=(0:30)/30,x3=(0:30)/30) pred < predict.gam(b,newd) ## now get variance of sum of predictions using lpmatrix Xp < predict(b,newd,type="lpmatrix") ## Xp %*% coef(b) yields vector of predictions a < rep(1,31) Xs < t(a) %*% Xp ## Xs %*% coef(b) gives sum of predictions var.sum < Xs %*% b$Vp %*% t(Xs) ## Now get the variance of nonlinear function of predictions ## by simulation from posterior distribution of the params library(MASS) br<mvrnorm(1000,coef(b),b$Vp) ## 1000 replicate param. vectors res < rep(0,1000) for (i in 1:1000) { pr < Xp %*% br[i,] ## replicate predictions res[i] < sum(log(abs(pr))) ## example nonlinear function } mean(res);var(res) ## loop is replaceable by following .... res < colSums(log(abs(Xp %*% t(br)))) ## The following shows how to use use an "lpmatrix" as a lookup ## table for approximate prediction. The idea is to create ## approximate prediction matrix rows by appropriate linear ## interpolation of an existing prediction matrix. The additivity ## of a GAM makes this possible. ## There is no reason to ever do this in R, but the following ## code provides a useful template for predicting from a fitted ## gam *outside* R: all that is needed is the coefficient vector ## and the prediction matrix. Use larger `Xp'/ smaller `dx' and/or ## higher order interpolation for higher accuracy. xn < c(.341,.122,.476,.981) ## want prediction at these values x0 < 1 ## intercept column dx < 1/30 ## covariate spacing in `newd' for (j in 0:2) { ## loop through smooth terms cols < 1+j*9 +1:9 ## relevant cols of Xp i < floor(xn[j+1]*30) ## find relevant rows of Xp w1 < (xn[j+1]i*dx)/dx ## interpolation weights ## find approx. predict matrix row portion, by interpolation x0 < c(x0,Xp[i+2,cols]*w1 + Xp[i+1,cols]*(1w1)) } dim(x0)<c(1,28) fv < x0%*%coef(b) + xn[4];fv ## evaluate and add offset se < sqrt(x0%*%b$Vp%*%t(x0));se ## get standard error ## compare to normal prediction predict(b,newdata=data.frame(x0=xn[1],x1=xn[2], x2=xn[3],x3=xn[4]),se=TRUE)