smooth.construct.po.smooth.spec: Constructor for SCOP-splines with positivity constraint
In scam: Shape Constrained Additive Models

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

smooth.construct.po.smooth.spec

R Documentation

Constructor for SCOP-splines with positivity constraint

Description

This is a special method function for creating univariate smooths subject to a positivity constraint which is built by the mgcv constructor function for smooth terms, smooth.construct. It is constructed using P-splines. This smooth is specified via model terms such as s(x,k,bs="po",m=2), where k denotes the basis dimension and m+1 is the order of the B-spline basis. Increasing and positive SCOP-splines are specified by model terms like s(x,bs="ipo"). Model terms s(x,bs="dpo") specify decreasing and positive SCOP-splines. Cyclic and positive splines are specified by s(x,bs="cpop").

Note: Models that include positive-valued smooth should not have an intercept. See examples below.

Usage

## S3 method for class 'po.smooth.spec'
smooth.construct(object, data, knots)
## S3 method for class 'ipo.smooth.spec'
smooth.construct(object, data, knots)
## S3 method for class 'dpo.smooth.spec'
smooth.construct(object, data, knots)
## S3 method for class 'cpop.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 "po.smooth", "ipo.smooth", "dpo.smooth", "cpop.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

 
## example with positivity constraint... 
## simulating data...
## Not run: 
   require(scam)
   set.seed(3)
   n <- 100
   x <- seq(-3,3,length.out=100)
   f <- dnorm(x) 
   y <- f + rnorm(n)*0.1  
   b <- scam(y~s(x,bs="po")-1)
  
   b1 <- scam(y~s(x)) ## unconstrained model
   plot(x,y)
   lines(x,f)
   lines(x,fitted(b),col=2)
   lines(x,fitted(b1),col=3)

  ## two-term example...
  set.seed(3)
  n <- 200
  x1 <- seq(-3,3,length.out=n)
  f1 <- 3*exp(-x1^2) ## positively constrained smooth
  x2 <- runif(n)*3-1;
  f2 <- exp(4*x2)/(1+exp(4*x2)) ## increasing smooth 
  f <- f1+f2
  y <- f+rnorm(n)*0.3
  dat <- data.frame(x1=x1,x2=x2,y=y)
  ## fit model, results, and plot...
  b2 <- scam(y~s(x1,bs="po")+s(x2,bs="mpi")-1,data=dat)
  summary(b2)
  plot(b2,pages=1)

  b3 <- scam(y~s(x1,bs="ps")+s(x2,bs="ps"),data=dat) ## unconstrained model
  summary(b3)
  plot(b3,pages=1) 
  
  ## three-term example: decreasing positive, cyclic positive, piece-wise linear positive...  
  set.seed(3)
  n <- 200
  x1 <- runif(n)*3-1
  f1 <- exp(-1.3*x1)# decreasing positive smooth 
  x2 <-  runif(200)*10
  f2 <- sin(x2*2*pi/10)+1 ## cyclic positive
  x3 <- f3 <- seq(0.34,1.9,length.out=n)  ## for piece-wise linear positive
  ind <- x3 > 1
  f3[!ind] <- 3*x3[!ind] -1 
  f3[ind] <- -2*x3[ind] +4 
  y <- f1+f2+f3 + rnorm(n)*.7
  b <- scam(y ~ s(x1,bs="dpo") +s(x2,bs="cpop",k=7)+ s(x3,bs="po",m=0,k=5) -1 )
  plot(b,pages=1) 
 
## End(Not run)

scam documentation built on April 3, 2025, 9:30 p.m.