Type:	Package
Title:	Function-on-Scalar Regression with Group-Bridge Penalty
Version:	0.9.2
License:	MIT + file LICENSE
Description:	Implements a group-bridge penalized function-on-scalar regression model proposed by Wang et al. (2023) <doi:10.1111/biom.13684>, to simultaneously estimate functional coefficient and recover the local sparsity.
URL:	https://github.com/dipterix/spfda, https://dipterix.org/spfda/
BugReports:	https://github.com/dipterix/spfda/issues
Imports:	stats, splines, graphics, mathjaxr
Encoding:	UTF-8
RoxygenNote:	7.3.2
RdMacros:	mathjaxr
BuildManual:	TRUE
Language:	en-US
Suggests:	grpreg, refund
NeedsCompilation:	no
Packaged:	2025-05-07 21:25:19 UTC; dipterix
Author:	Zhengjia Wang [aut, cre], Meng Li [aut]
Maintainer:	Zhengjia Wang <dipterix.wang@gmail.com>
Repository:	CRAN
Date/Publication:	2025-05-07 21:40:02 UTC

Ported function from 'refund' package

Description

A modified version of fosr.vs, but with groups parameter to allow grouping time points rather than the whole coefficient when the underlying functions are locally supported.

Usage

fosr_vs(
  formula,
  data,
  nbasis = 10,
  method = c("ls", "grLasso", "grMCP", "grSCAD"),
  epsilon = 1e-05,
  max.iter_num = 100,
  groups = NULL
)

Arguments

Sparse Function-on-scalar Regression with Group Bridge Penalty

Description

Function-on-scalar regression model, denote \(n\) as total number of observations, \(p\) the number of coefficients, \(K\) as the number of B-splines, \(T\) as total time points.

Usage

spfda(
  Y,
  X,
  lambda,
  time = seq(0, 1, length.out = ncol(Y)),
  nsp = "auto",
  ord = 4,
  alpha = 0.5,
  W = NULL,
  init = NULL,
  max_iter = 50,
  inner_iter = 50,
  CI = FALSE,
  ...
)

Arguments

Details

This function implements "Functional Group Bridge for Simultaneous Regression and Support Estimation" (doi:10.1111/biom.13684). The model estimates functional coefficients \(\beta(t)\) under model \[y(t) = X\beta(t) + \epsilon(t)\] with B-spline basis expansion \[\beta(t) = \gamma B(t) + R(t), \] where \( R(t) \) is B-spline approximation error. The objective function \[ \left\| (Y-X\gamma B)W \right\|_{2}^{2} + \sum_{j,m} \left\| \gamma_{j}^{T}\mathbf{1}(B^{t} > 0) \right\|_{1}^{\alpha}. \] The input response variable is a matrix. If \(y_{i}(t)\) are observed at different time points, please interpolate (e.g. kernel) before feeding in.

Value

A spfda.model object (environment) with following elements:

B

B-spline basis functions used

error

Root Mean Square Error ('RMSE')

CI

Whether confidence intervals are calculated

gamma

B-spline coefficient \(\gamma_{p \times K}\)

generate_splines

Function to generate B-splines given time points

K

Number of B-spline basis functions

knots

B-spline knots used to fit the model

predict

Function to predict responses \(\beta(t)\) given new X and/or time points

raw

A list of raw variables

Examples

dat <- spfda_simulate()
x <- dat$X
y <- dat$Y

fit <- spfda(y, x, lambda = 5, CI = TRUE)

BIC(fit)

plot(fit, col = c("orange", "dodgerblue3", "darkgreen"),
     main = "Fitted with 95% CI", aty = c(0, 0.5, 1), atx = c(0,0.2,0.8,1))
matpoints(fit$time, t(dat$env$beta), type = 'l', col = 'black', lty = 2)
legend('topleft', c("Fitted", "Underlying"), lty = c(1,2))

print(fit)
coefficients(fit)

Generates toy example data

Description

Synthesized functional signals with heterogeneous error. The underlying three coefficients correspond to 'dense', 'global sparse', and 'local sparse' functions. See doi:10.1111/biom.13684 for detailed configurations.

Usage

spfda_simulate(n = 1000, n_timepoints = 100, err = 1, scale = c(1, 1, 1))

Arguments

Value

A list of data generated: X is scalar predictor, Y is functional response.

Calculates weight matrices

Description

Calculates weight matrices

Usage

spfda_weight(X, Y, bandwidth, part)

Arguments

Value

the weight matrix