spfda: Sparse Function-on-scalar Regression with Group Bridge...

In spfda: Function-on-Scalar Regression with Group-Bridge Penalty

Sparse Function-on-scalar Regression with Group Bridge Penalty

Description

\loadmathjax

Function-on-scalar regression model, denote \mjseqnn as total number of observations, \mjseqnp the number of coefficients, \mjseqnK as the number of B-splines, \mjseqnT 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

Y	Numeric \mjseqnn \times T matrix, response function.
X	Numeric \mjseqnn \times p matrix, design matrix
lambda	Regularization parameter \mjseqn\gamma
time	Time domain, numerical length of \mjseqnT
nsp	Integer or 'auto', number of B-splines \mjseqnK; default is 'auto'
ord	B-spline order, default is 4; must be \mjseqn\geq 3
alpha	Bridge parameter \mjseqn\alpha, default is 0.5
W	A \mjseqnT \times T weight matrix or NULL (identity matrix); default is NULL
init	Initial \mjseqn\gamma; default is NULL
max_iter	Number of outer iterations
inner_iter	Number of \mjseqnADMM iterations (inner steps)
CI	Logical, whether to calculate theoretical confidence intervals
...	Ignored

Details

This function implements "Functional Group Bridge for Simultaneous Regression and Support Estimation" (https://arxiv.org/abs/2006.10163). The model estimates functional coefficients \mjseqn\beta(t) under model \mjsdeqny(t) = X\beta(t) + \epsilon(t) with B-spline basis expansion \mjsdeqn\beta(t) = \gamma B(t) + R(t), where \mjseqn R(t) is B-spline approximation error. The objective function \mjsdeqn \left\| (Y-X\gamma B)W \right\|_2^2 + \sum_j,m \left\| \gamma_j^T\mathbf1(B^t > 0) \right\|_1^\alpha. The input response variable is a matrix. If \mjseqny_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 \mjseqn\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 \mjseqn\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)

spfda documentation built on March 18, 2022, 6:57 p.m.