smooth.construct.cv.smooth.spec: Constructor for concave P-splines in SCAMs
In scam: Shape Constrained Additive Models

View source: R/uni.smooth.const-with-po.r

smooth.construct.cv.smooth.spec

R Documentation

Constructor for concave P-splines in SCAMs

Description

This is a special method function for creating smooths subject to concavity constraint which is built by the mgcv constructor function for smooth terms, smooth.construct. It is constructed using concave P-splines. This smooth is specified via model terms such as s(x,k,bs="cv",m=2), where k denotes the basis dimension and m+1 is the order of the B-spline basis.

cvBy.smooth.spec works similar to cv.smooth.spec but without applying an identifiability constraint ('zero intercept' constraint). cvBy.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="cvBy"). See an example below.

However a factor by variable requires identifiability constraints, so s(x,by=fac,bs="cv") is used in this case.

Usage

## S3 method for class 'cv.smooth.spec'
smooth.construct(object, data, knots)
## S3 method for class 'cvBy.smooth.spec'
smooth.construct(object, data, knots)

Arguments

`object`	A smooth specification object, generated by an `s` term in a GAM formula.
`data`	A data frame or list containing the data required by this term, with names given by `object$term`. The `by` variable is the last element.
`knots`	An optional list containing the knots supplied for basis setup. If it is `NULL` then the knot locations are generated automatically.

Value

An object of class "cv.smooth", "cvBy.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

Examples

 ## Not run: 
## Concave P-splines example 
  ## simulating data...
   require(scam)
   set.seed(1)
   n <- 100
   x <- sort(2*runif(n)-1)
   f <- -4*x^2
   y <- f + rnorm(n)*0.45
   dat <- data.frame(x=x,y=y)
   b <- scam(y~s(x,k=15,bs="cv"),family=gaussian,data=dat,not.exp=FALSE)
   ## fit unconstrained model...
   b1 <- scam(y~s(x,k=15,bs="cr"),family=gaussian, data=dat,not.exp=FALSE)
   ## plot results ...
   plot(x,y,xlab="x",ylab="y",cex=.5)
   lines(x,f)      ## the true function
   lines(x,b$fitted,col=2)  ## constrained fit 
   lines(x,b1$fitted,col=3) ## unconstrained fit 

## Poisson version...
   y <- rpois(n,15*exp(f))
   dat <- data.frame(x=x,y=y)
   ## fit model ...
   b <- scam(y~s(x,k=15,bs="cv"),family=poisson(link="log"),data=dat,not.exp=FALSE)

   ## fit unconstrained model...
   b1<-scam(y~s(x,k=15,bs="cr"),family=poisson(link="log"), data=dat,not.exp=FALSE)
   ## plot results ...
   plot(x,y,xlab="x",ylab="y",cex=.5)
   lines(x,15*exp(f))      ## the true function
   lines(x,b$fitted,col=2)  ## constrained fit 
   lines(x,b1$fitted,col=3) ## unconstrained fit 

## plotting on log scale...
   plot(x,log(15*exp(f)),type="l",cex=.5)      ## the true function
   lines(x,log(b$fitted),col=2)  ## constrained fit 
   lines(x,log(b1$fitted),col=3) ## unconstrained fit 

## 'by' factor example... 
  set.seed(9)
  n <- 400
  x <- sort(runif(n,-.5,.5))
  f1 <- -.7*x+cos(x)-3
  f2 <- -20*x^2 
  par(mfrow=c(1,2))
  plot(x,f1,type="l");plot(x,f2,type="l")
  e <- rnorm(n, 0, 1.5)
  fac <- as.factor(sample(1:2,n,replace=TRUE))
  fac.1 <- as.numeric(fac==1)
  fac.2 <- as.numeric(fac==2)
  y <- f1*fac.1 + f2*fac.2 + e 
  dat <- data.frame(y=y,x=x,fac=fac,f1=f1,f2=f2)
  b2 <- scam(y ~ fac+s(x,by=fac,bs="cv"),data=dat,optimizer="efs")  
  plot(b2,pages=1,scale=0,shade=TRUE)
  summary(b2)
  x11()
  vis.scam(b2,theta=50,color="terrain")

 ## numeric 'by' variable example... 
 set.seed(6)
 n <- 100
 x <- sort(2*runif(n)-1)
 z <- runif(n,-2,3)
 f <- -4*x^2
 y <- f*z + rnorm(n)*0.6
 dat <- data.frame(x=x,z=z,y=y)
 b <- scam(y~s(x,k=15,by=z,bs="cvBy"),data=dat)
 summary(b)
 par(mfrow=c(1,2))
 plot(b,shade=TRUE)
 ## unconstrained fit...
 b1 <- scam(y~s(x,k=15,by=z),data=dat)
 plot(b1,shade=TRUE)
 summary(b1)
  
## End(Not run)

scam documentation built on June 22, 2024, 10:43 a.m.