Function-on-Scalar Regression

Functions for regression where the response is a function and predictors are scalar variables. Function-on-Scalar Regression (Penalized)

Usage

fosr(fdataobj, predictors, lambda = 0)

Arguments

fdataobj: An object of class 'fdata' (functional response).
predictors: A matrix of scalar predictors (n x p).
lambda: Smoothing/penalty parameter (default 0).

Value

An object of class 'fosr' with components:

intercept: Intercept function mu(t) as fdata
beta: Coefficient functions beta_j(t) as fdata
fitted: Fitted functional values as fdata
residuals: Residual functions as fdata
r.squared: Global R-squared
r.squared.t: Pointwise R-squared
gcv: GCV criterion value
lambda: Smoothing parameter used

Details

Fits a penalized function-on-scalar regression model where the response is a function Y_i(t) and predictors are scalar: Y_i(t) = mu(t) + sum_j x_ij beta_j(t) + eps_i(t).

Examples

# \donttest{
# Functional response: 50 curves observed at 10 time points
Y <- fdata(matrix(rnorm(500), 50, 10), argvals = seq(0, 1, length.out = 10))
# Two scalar predictors
X <- cbind(rnorm(50), rnorm(50))
fit <- fosr(Y, predictors = X, lambda = 1)
fit
#> Function-on-Scalar Regression
#> =============================
#>   Number of observations: 50 
#>   Number of predictors: 2 
#>   Evaluation points: 10 
#>   R-squared: 0.0451 
#>   Lambda: 1 
# }