| smooth.construct.mpi.smooth.spec {scam} | R Documentation |
Constructor for monotone increasing P-splines in SCAMs
Description
This is a special method function
for creating smooths subject to a monotone increasing constraint 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="mpi",m=2),
where k denotes the basis dimension and m+1 is the order of the B-spline basis.
mpiBy.smooth.spec works similar to mpi.smooth.spec but without applying an identifiability constraint ('zero intercept' constraint). mpiBy.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="mpiBy"). See an example below.
However a factor by variable requires identifiability constraints, so s(x,by=fac,bs="mpi") is used in this case.
Usage
## S3 method for class 'mpi.smooth.spec'
smooth.construct(object, data, knots)
## S3 method for class 'mpiBy.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 |
Details
The constructor is not called directly, but as with gam(mgcv) is used internally.
If the knots of the spline are not supplied, then they are placed evenly throughout the covariate values. If the knots are supplied, then the number of supplied knots should be k+m+2, and the range of the middle k-m knots must include all the covariate values.
Value
An object of class "mpi.smooth", "mpiBy.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.mpd.smooth.spec,
smooth.construct.cv.smooth.spec,
smooth.construct.cx.smooth.spec,
smooth.construct.mdcv.smooth.spec,
smooth.construct.mdcx.smooth.spec,
smooth.construct.micv.smooth.spec,
smooth.construct.micx.smooth.spec
Examples
## Monotone increasing P-splines example
## simulating data...
require(scam)
set.seed(12)
n <- 100
x <- runif(n)*4-1
f <- 4*exp(4*x)/(1+exp(4*x))
y <- rpois(n,exp(f))
dat <- data.frame(x=x,y=y)
## fit model ...
b <- scam(y~s(x,k=15,bs="mpi"),family=poisson(link="log"),
data=dat)
## fit unconstrained model...
b1 <- scam(y~s(x,k=15,bs="ps"),family=poisson(link="log"),
data=dat)
## plot results ...
plot(x,y,xlab="x",ylab="y")
x1 <- sort(x,index=TRUE)
lines(x1$x,exp(f)[x1$ix]) ## the true function
lines(x1$x,b$fitted.values[x1$ix],col=2) ## monotone fit
lines(x1$x,b1$fitted.values[x1$ix],col=3) ## unconstrained fit
## example with supplied knots...
knots <- list(x=c (-1.5, -1.2, -.99, -.97, -.7, -.5, -.3, 0, 0.7,
0.9,1.1, 1.22,1.5,2.2,2.77,2.93,2.99, 3.2,3.6))
b2 <- scam(y~s(x,k=15,bs="mpi"),knots=knots,
family=poisson(link="log"), data=dat)
summary(b2)
plot(b2,shade=TRUE)
## Not run:
## example with two terms...
set.seed(0)
n <- 200
x1 <- runif(n)*6-3
f1 <- 3*exp(-x1^2) # unconstrained term
x2 <- runif(n)*4-1;
f2 <- exp(4*x2)/(1+exp(4*x2)) # monotone increasing smooth
f <- f1+f2
y <- f+rnorm(n)*.7
dat <- data.frame(x1=x1,x2=x2,y=y)
knots <- list(x1=c(-4,-3.5,-2.99,-2.7,-2.5,-1.9,-1.1,-.9,-.3,0.3,.8,1.2,1.9,2.3,
2.7,2.99,3.5,4.1,4.5), x2=c(-1.5,-1.2,-1.1, -.89,-.69,-.5,-.3,0,0.7,
0.9,1.1,1.22,1.5,2.2,2.77,2.99,3.1, 3.2,3.6))
b3 <- scam(y~s(x1,k=15)+s(x2,bs="mpi", k=15),
knots=knots,data=dat)
summary(b3)
plot(b3,pages=1,shade=TRUE)
## setting knots for f(x2) only...
knots <- list(x2=c(-1.5,-1.2,-1.1, -.89,-.69,-.5,-.3,
0,0.7,0.9,1.1,1.22,1.5,2.2,2.77,2.99,3.1, 3.2,3.6))
b4 <- scam(y~s(x1,k=15,bs="bs")+s(x2,bs="mpi",k=15),
knots=knots,data=dat)
summary(b4)
plot(b4,pages=1,shade=TRUE)
## 'by' factor example...
set.seed(10)
n <- 400
x <- runif(n, 0, 1)
## all three smooths are increasing...
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)
b5 <- scam(y ~ fac+s(x,by=fac,bs="mpi"),data=dat)
plot(b5,pages=1,scale=0,shade=TRUE)
summary(b5)
vis.scam(b5,theta=50,color="terrain")
## comparing with unconstrained fit...
b6 <- scam(y ~ fac+s(x,by=fac),data=dat)
x11()
plot(b6,pages=1,scale=0,shade=TRUE)
summary(b6)
vis.scam(b6,theta=50,color="terrain")
## 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 <- 200
x <- sort(runif(n,-1,2))
z <- runif(n,-2,3)
f <- exp(1.3*x)-5
y <- f*z + rnorm(n)*2
dat <- data.frame(x=x,y=y,z=z)
b <- scam(y~s(x,by=z,bs="mpiBy"),data=dat)
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)