scam (version 1.2-17)

linear.functional.terms: Linear functionals of a smooth in GAMs

Description

Since scam uses the model setup of gam of the mgcv package, in the same way as in gam scam allows the response variable to depend on linear functionals of smooth terms in the s with additional shape constraints.

See linear.functional.terms(mgcv).

Examples

 if (FALSE) {
###########################################
## similar to a "signal" regression 
## example from mgcv() ...
###########################################
library(scam)
## decreasing smooth...
set.seed(4)
rf <- function(x=seq(-1,3,length=100)) { ## taken from mgcv package
## generates random functions...
  m <- ceiling(runif(1)*5) ## number of components
  f <- x*0;
  mu <- runif(m,min(x),max(x)); sig <- (runif(m)+.5)*(max(x)-min(x))/10
  for (i in 1:m) f <- f+ dnorm(x,mu[i],sig[i])
  f
}

## simulate 200 functions and store in rows of L...
L <- matrix(NA,200,100) 
for (i in 1:200) L[i,] <- rf()  ## simulate the functional predictors

x <- seq(-1,3,length=100) ## evaluation points
f2 <- function(x) { ## the coefficient function
     -4*exp(4*x)/(1+exp(4*x))  
}
f <- f2(x) 
plot(x,f ,type="l")
y <- L%*%f + rnorm(200)*20 ## simulated response data
X <- matrix(x,200,100,byrow=TRUE) 

b <- scam(y~s(X,by=L,k=20,bs="mpdBy")) 
par(mfrow=c(1,2))
plot(b,shade=TRUE);lines(x,f,col=2); 
## compare with gam() of mgcv package...
g <- gam(y~s(X,by=L,k=20)) 
plot(g,shade=TRUE);lines(x,f,col=2)


## increasing smooth....
L <- matrix(NA,200,100) 
for (i in 1:200) L[i,] <- rf()  ## simulate the functional predictors
x <- seq(-1,3,length=100) ## evaluation points
f2 <- function(x) { ## the coefficient function
     4*exp(4*x)/(1+exp(4*x))  
}
f <- f2(x) 
plot(x,f ,type="l")
y <- L%*%f + rnorm(200)*20 ## simulated response data
X <- matrix(x,200,100,byrow=TRUE) 
b <- scam(y~s(X,by=L,k=20,bs="mpiBy")) 
par(mfrow=c(1,2))
plot(b,shade=TRUE);lines(x,f,col=2); 
## compare with unconstrained fit...
g <- scam(y~s(X,by=L,k=20)) 
plot(g,shade=TRUE);lines(x,f,col=2)


## convex smooth...
 ## simulate 200 functions and store in rows of L...
set.seed(4)
L <- matrix(NA,200,100) 
for (i in 1:200) L[i,] <- rf(x=sort(2*runif(100)-1))  ## simulate the functional predictors

x <- sort(runif(100,-1,1)) ## evaluation points
f2 <- function(x){4*x^2 } ## the coefficient function
f <- f2(x) 
plot(x,f ,type="l")
y <- L%*%f + rnorm(200)*30 ## simulated response data
X <- matrix(x,200,100,byrow=TRUE) 

b <- scam(y~s(X,by=L,k=20,bs="cxBy")) 
par(mfrow=c(1,2))
plot(b,shade=TRUE);lines(x,f,col=2); 

g <- scam(y~s(X,by=L,k=20)) 
plot(g,shade=TRUE);lines(x,f,col=2)

 }