smooth.construct.miso.smooth.spec: Constructor for monotone increasing SCOP-splines with an...
In scam: Shape Constrained Additive Models

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

smooth.construct.miso.smooth.spec

R Documentation

Constructor for monotone increasing SCOP-splines with an additional 'start at zero' constraint

Description

This is a special method function for creating smooths subject to a monotone increasing constraint plus the smooths should pass through zero at the left-end point of the covariate range. This is similar to the pc argument to s in mgcv(gam) when pc=min(x), where x is a covariate. The smooth is built by the mgcv constructor function for smooth terms, smooth.construct. 'Zero intercept' identifiability constraints used for univariate SCOP-splines are substituted with a 'start at zero' constraint here. This smooth is specified via model terms such as s(x,k,bs="miso",m=2), where k denotes the basis dimension and m+1 is the order of the B-spline basis.

Usage

## S3 method for class 'miso.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.

Details

The constructor is not called directly, but as with gam(mgcv) is used internally.

A 'start at zero' constraint is achieved by setting the first (m+1) spline coefficients to zero. According to the B-spline basis functions properties, the value of the spline, f(x), is determined by m+2 non-zero basis functions, and only m+1 B-splines are non-zero at knots. Only m+2 B-splines are non-zero on any [k_i, k_{i+1}), and the sum of these m+2 basis functions is 1.

If the knots of the spline are not supplied, then they are placed evenly throughout the covariate values with an exception of the m inner knots following the first inner knot that are joined with that first knot. This is done in order to avoid an otherwise plateau fit at the left-end region. 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 "miso.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

 
  ## Monotone increasing SCOP-spline examples with a start at zero constraint...
  ## passing through 0 at -1...
  require(scam)
  set.seed(7)
  n <- 100;
  x <- c(-1,runif(n-1)*4-1); ## starting at -1 for a function to be zero at a start
  z <- runif(n)
  y <- exp(4*x)/(1+exp(4*x)) -0.01798621+ z*(1-z)*5 + rnorm(100)*.4
  m1 <- scam(y~s(x,bs='miso')+s(z)) 
  plot(m1,pages=1)
  newd<- data.frame(x=-1,z=0)
  predict(m1,newd, type='terms')


## Not run: 
  ## passing through 0 at 0...
  set.seed(53)
  n <- 100;
  x <- c(0,runif(n-1)); ## starting at 0 for a function to be zero at a start
  z <- runif(n)
  y <- exp(3*x)/10-.1 + z*(1-z)*5 + rnorm(100)*.4
  m2 <- scam(y~s(x,bs='miso')+s(z)) 
  plot(m2,pages=1)
  newd<- data.frame(x=0,z=0)
  predict(m2,newd, type='terms')

    
## End(Not run)

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