refund: fosr.vs – R documentation

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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.

Author(s)

Yakuan Chen yc2641@cumc.columbia.edu

References

Chen, Y., Goldsmith, J., and Ogden, T. (2016). Variable selection in function-on-scalar regression. Stat 5 88-101

Examples

## Not run: 
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)

## End(Not run)

refund

Regression with Functional Data

v0.1-23

GPL (>= 2)

Authors

Jeff Goldsmith [aut], Fabian Scheipl [aut], Lei Huang [aut], Julia Wrobel [aut, cre], Chongzhi Di [aut], Jonathan Gellar [aut], Jaroslaw Harezlak [aut], Mathew W. McLean [aut], Bruce Swihart [aut], Luo Xiao [aut], Ciprian Crainiceanu [aut], Philip T. Reiss [aut], Yakuan Chen [ctb], Sonja Greven [ctb], Lan Huo [ctb], Madan Gopal Kundu [ctb], So Young Park [ctb], David L. Miller [ctb], Ana-Maria Staicu [ctb]

Initial release

2020-12-03