refund (version 0.1-1)

fosr.vs: Function-on Scalar Regression with variable selection

Description

Implements an iterative algorithm for function-on-scalar regression with variable selection by alternatively updating the coefficients and covariance structure.

Usage

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

Arguments

formula

an object of class "formula": an expression of the model to be fitted.

data

a data frame that contains the variables in the model.

nbasis

number of B-spline basis functions used.

method

group variable selection method to be used ("grLasso", "grMCP", "grSCAD" refer to group Lasso, group MCP and group SCAD, respectively) or "ls" for least squares estimation.

epsilon

the convergence criterion.

max.iter_num

maximum number of iterations.

Value

• A fitted fosr.vs-object, which is a list with the following elements:
• formula
  an object of class "formula": an expression of the model to be fitted.
• coefficients
  the estimated coefficient functions.
• fitted.values
  the fitted curves.
• residuals
  the residual curves.
• vcov
  the estimated variance-covariance matrix when convergence is achieved.
• method
  group variable selection method to be used or "ls" for least squares estimation.

References

Chen, Y., Goldsmith, J., and Ogden, T. (under review). Variable selection in function-on-scalar regression.

See Also

grpreg

Examples

set.seed(100)

I = 100
p = 20
D = 50
grid = seq(0, 1, length = D)

beta.true = matrix(0, p, D)
beta.true[1,] = sin(2*grid*pi)
beta.true[2,] = cos(2*grid*pi)
beta.true[3,] = 2

psi.true = matrix(NA, 2, D)
psi.true[1,] = sin(4*grid*pi)
psi.true[2,] = cos(4*grid*pi)
lambda = c(3,1)

set.seed(100)

X = matrix(rnorm(I*p), I, p)
C = cbind(rnorm(I, mean = 0, sd = lambda[1]), rnorm(I, mean = 0, sd = lambda[2]))

fixef = X%*%beta.true
pcaef = C %*% psi.true
error = matrix(rnorm(I*D), I, D)

Yi.true = fixef
Yi.pca = fixef + pcaef
Yi.obs = fixef + pcaef + error

data = as.data.frame(X)
data$Y = Yi.obs
fit.fosr.vs = fosr.vs(Y~., data = data, method="grMCP")
plot(fit.fosr.vs)