refund (version 0.1-3)

pfr: Penalized Functional Regression

Description

Implements penalized functional regression (Goldsmith et al. 2011) for generalized linear functional models with scalar outcomes.

Usage

pfr(Y, covariates = NULL, funcs, kz = 30, kb = 30, smooth.cov = FALSE, family = "gaussian", ...)

Arguments

Y

Length n vector of outcomes

covariates

n by p matrix of scalar covariates

funcs

n by N matrix of observed functional predictors

kz

Dimension of principal components basis for the observed functional predictors

kb

Dimension of the truncated power series spline basis for the coefficient function

smooth.cov

Logical; do you wish to smooth the covariance matrix of observed functions? Increases computation time, but results in smooth principal components

family

Generalized linear model family

...

Additional arguments passed to the gam function to fit the regression model.

Value

• gam
  The result of the call to gam
• fitted.vals
  Predicted outcomes
• betaHat
  Estimated coefficient function
• beta.covariates
  Parameter estimates for scalar covariates
• X
  Design matrix used in the model fit
• phi
  Truncated power series spline basis for the coefficient function
• psi
  Principal components basis for the functional predictors
• varBetaHat
  Covariance matrix for the estimated coefficient function
• Bounds
  Bounds of a 95% confidence interval for the estimated coefficient function

References

Goldsmith, J., Bobb, J., Crainiceanu, C., Caffo, B., and Reich, D. (2011). Penalized functional regression. Journal of Computational and Graphical Statistics, to appear.

Examples

##### Octane Data Example #####
data(gasoline)
Y = gasoline$octane
funcs = gasoline$NIR
wavelengths = 2*450:850

# fit the model using pfr
fit = pfr(Y=Y, funcs=funcs, kz=50, kb=50)

# plot the estimated coefficient function
matplot(wavelengths, cbind(fit$betaHat, fit$Bound), type='l', lwd=c(2,1,1), 
    lty=c(1,2,2), xlab = "Wavelengths", ylab = "Coefficient Function", col=1)