| smooth.construct.mpd.smooth.spec {scam} | R Documentation |
Constructor for monotone decreasing P-splines in SCAMs
Description
This is a special method function
for creating smooths subject to monotone decreasing constraints which is built by
the mgcv constructor function for smooth terms, smooth.construct.
It is constructed using monotonic P-splines. This smooth is specified via model terms such as
s(x,k,bs="mpd",m=2),
where k denotes the basis dimension and m+1 is the order of the B-spline basis.
mpdBy.smooth.spec works similar to mpd.smooth.spec but without applying an identifiability constraint ('zero intercept' constraint). mpdBy.smooth.spec should be used when the smooth term has a numeric by variable that takes more than one value. In such cases, the smooth terms are fully identifiable without a 'zero intercept' constraint, so they are left unconstrained. This smooth is specified as
s(x,by=z,bs="mpdBy"). See an example below.
However a factor by variable requires identifiability constraints, so s(x,by=fac,bs="mpd") is used in this case.
Usage
## S3 method for class 'mpd.smooth.spec'
smooth.construct(object, data, knots)
## S3 method for class 'mpdBy.smooth.spec'
smooth.construct(object, data, knots)
Arguments
object |
A smooth specification object, generated by an |
data |
A data frame or list containing the data required by this term,
with names given by |
knots |
An optional list containing the knots supplied for basis setup.
If it is |
Value
An object of class "mpd.smooth", "mpdBy.smooth".
Author(s)
Natalya Pya <nat.pya@gmail.com>
References
Pya, N. and Wood, S.N. (2015) Shape constrained additive models. Statistics and Computing, 25(3), 543-559
Pya, N. (2010) Additive models with shape constraints. PhD thesis. University of Bath. Department of Mathematical Sciences
See Also
smooth.construct.mpi.smooth.spec,
smooth.construct.cx.smooth.spec,
smooth.construct.cv.smooth.spec,
smooth.construct.mdcv.smooth.spec,
smooth.construct.mdcx.smooth.spec,
smooth.construct.micv.smooth.spec,
smooth.construct.micx.smooth.spec
Examples
## Not run:
## Monotone decreasing SCOP-splines example...
## simulating data...
require(scam)
set.seed(3)
n <- 100
x <- runif(n)*3-1
f <- exp(-1.3*x)
y <- rpois(n,exp(f))
dat <- data.frame(x=x,y=y)
## fit model ...
b <- scam(y~s(x,k=15,bs="mpd"),family=poisson(link="log"),
data=dat)
## unconstrained model fit for comparison...
b1 <- scam(y~s(x,k=15,bs="ps"),family=poisson(link="log"),
data=dat)
## plot results ...
plot(x,y,xlab="x",ylab="y",cex=.5)
x1 <- sort(x,index=TRUE)
lines(x1$x,exp(f)[x1$ix]) ## the true function
lines(x1$x,b$fitted.values[x1$ix],col=2) ## decreasing fit
lines(x1$x,b1$fitted.values[x1$ix],col=3) ## unconstrained fit
## 'by' factor example...
set.seed(3)
n <- 400
x <- runif(n, 0, 1)
## all three smooths are decreasing...
f1 <- -log(x *5)
f2 <- -exp(2 * x) + 4
f3 <- -5* sin(x)
e <- rnorm(n, 0, 2)
fac <- as.factor(sample(1:3,n,replace=TRUE))
fac.1 <- as.numeric(fac==1)
fac.2 <- as.numeric(fac==2)
fac.3 <- as.numeric(fac==3)
y <- f1*fac.1 + f2*fac.2 + f3*fac.3 + e
dat <- data.frame(y=y,x=x,fac=fac,f1=f1,f2=f2,f3=f3)
b2 <- scam(y ~ fac+s(x,by=fac,bs="mpd"),data=dat)
plot(b2,pages=1,scale=0,shade=TRUE)
summary(b2)
vis.scam(b2,theta=120,color="terrain")
## comparing with unconstrained fit...
b3 <- scam(y ~ fac+s(x,by=fac),data=dat)
x11()
plot(b3,pages=1,scale=0,shade=TRUE)
summary(b3)
## Note that since in scam() as in mgcv::gam() when using factor 'by' variables, 'centering'
## constraints are applied to the smooths, which usually means that the 'by'
## factor variable should be included as a parametric term, as well.
## numeric 'by' variable example...
set.seed(3)
n <- 100
x <- sort(runif(n,-1,2))
z <- runif(n,-2,3)
f <- exp(-1.3*x)
y <- f*z + rnorm(n)*0.4
dat <- data.frame(x=x,y=y,z=z)
b <- scam(y~s(x,k=15,by=z,bs="mpdBy"),data=dat,optimizer="efs")
plot(b,shade=TRUE)
summary(b)
## unconstrained fit...
b1 <- scam(y~s(x,k=15,by=z),data=dat)
plot(b1,shade=TRUE)
summary(b1)
## End(Not run)