| sscden {gss} | R Documentation |
Estimate conditional probability densities using smoothing spline
ANOVA models. The symbolic model specification via formula
follows the same rules as in lm.
sscden(formula, response, type=NULL, data=list(), weights, subset,
na.action=na.omit, alpha=1.4, id.basis=NULL, nbasis=NULL,
seed=NULL, ydomain=as.list(NULL), yquad=NULL, prec=1e-7,
maxiter=30, skip.iter=FALSE)
sscden1(formula, response, type=NULL, data=list(), weights, subset,
na.action=na.omit, alpha=1.4, id.basis=NULL, nbasis=NULL,
seed=NULL, rho=list("xy"), ydomain=as.list(NULL), yquad=NULL,
prec=1e-7, maxiter=30, skip.iter=FALSE)
formula |
Symbolic description of the model to be fit. |
response |
Formula listing response variables. |
type |
List specifying the type of spline for each variable.
See |
data |
Optional data frame containing the variables in the model. |
weights |
Optional vector of counts for duplicated data. |
subset |
Optional vector specifying a subset of observations to be used in the fitting process. |
na.action |
Function which indicates what should happen when the data contain NAs. |
alpha |
Parameter defining cross-validation scores for smoothing parameter selection. |
id.basis |
Index of observations to be used as "knots." |
nbasis |
Number of "knots" to be used. Ignored when
|
seed |
Seed to be used for the random generation of "knots."
Ignored when |
ydomain |
Data frame specifying marginal support of conditional density. |
yquad |
Quadrature for calculating integral on Y domain. Mandatory if response variables other than factors or numerical vectors are involved. |
prec |
Precision requirement for internal iterations. |
maxiter |
Maximum number of iterations allowed for internal iterations. |
skip.iter |
Flag indicating whether to use initial values of
theta and skip theta iteration. See |
rho |
rho function needed for sscden1. |
The model is specified via formula and response, where
response lists the response variables. For example,
sscden(~y*x,~y) prescribe a model of the form
log f(y|x) = g_{y}(y) + g_{xy}(x,y) + C(x)
with the terms denoted by "y", "y:x"; the term(s) not
involving response(s) are removed and the constant C(x) is
determined by the fact that a conditional density integrates to one
on the y axis. sscden1 does keep terms not involving
response(s) during estimation, although those terms cancel out when
one evaluates the estimated conditional density.
The model terms are sums of unpenalized and penalized terms. Attached to every penalized term there is a smoothing parameter, and the model complexity is largely determined by the number of smoothing parameters.
A subset of the observations are selected as "knots." Unless
specified via id.basis or nbasis, the number of
"knots" q is determined by max(30,10n^{2/9}), which is
appropriate for the default cubic splines for numerical vectors.
sscden returns a list object of class "sscden".
sscden1 returns a list object of class
c("sscden1","sscden").
dsscden and cdsscden can be used to
evaluate the estimated conditional density f(y|x) and
f(y1|x,y2); psscden, qsscden,
cpsscden, and cqsscden can be used to
evaluate conditional cdf and quantiles. The methods
project.sscden or project.sscden1 can
be used to calculate the Kullback-Leibler or square-error
projections for model selection.
Default quadrature on the Y domain will be constructed for numerical
vectors on a hyper cube, then outer product with factor levels will
be taken if factors are involved. The sides of the hyper cube are
specified by ydomain; for ydomain$y missing, the default
is c(min(y),max(y))+c(-1,1)*(max(y)-mimn(y))*.05.
On a 1-D interval, the quadrature is the 200-point Gauss-Legendre
formula returned from gauss.quad. For multiple
numerical vectors, delayed Smolyak cubatures from
smolyak.quad are used on cubes with the marginals
properly transformed; see Gu and Wang (2003) for the marginal
transformations.
The results may vary from run to run. For consistency, specify
id.basis or set seed.
For reasonable execution time in high dimensions, set
skip.iter=TRUE.
Chong Gu, chong@stat.purdue.edu
Gu, C. (1995), Smoothing spline density estimation: Conditional distribution. Statistica Sinica, 5, 709–726. Springer-Verlag.
data(penny); set.seed(5732)
fit <- sscden(~year*mil,~mil,data=penny,
ydomain=data.frame(mil=c(49,61)))
yy <- 1944+(0:92)/2
quan <- qsscden(fit,c(.05,.25,.5,.75,.95),
data.frame(year=yy))
plot(penny$year+.1*rnorm(90),penny$mil,ylim=c(49,61))
for (i in 1:5) lines(yy,quan[i,])
## Clean up
## Not run: rm(penny,yy,quan)