refund (version 0.1-23)

# 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. (2016). Variable selection in function-on-scalar regression. Stat 5 88-101

`grpreg`

## 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)
# }
# NOT RUN {

# }
```