# gls_cs: Cross-sectional FoSR using GLS

## Description

Fitting function for function-on-scalar regression for cross-sectional data.
This function estimates model parameters using GLS: first, an OLS estimate of
spline coefficients is estimated; second, the residual covariance is estimated
using an FPC decomposition of the OLS residual curves; finally, a GLS estimate
of spline coefficients is estimated. Although this is in the `BayesFoSR` package,
there is nothing Bayesian about this FoSR.

## Usage

gls_cs(
formula,
data = NULL,
Kt = 5,
basis = "bs",
sigma = NULL,
verbose = TRUE,
CI.type = "pointwise"
)

## Arguments

formula

a formula indicating the structure of the proposed model.

data

an optional data frame, list or environment containing the
variables in the model. If not found in data, the variables are taken from
environment(formula), typically the environment from which the function is
called.

Kt

number of spline basis functions used to estimate coefficient functions

basis

basis type; options are "bs" for b-splines and "pbs" for periodic
b-splines

sigma

optional covariance matrix used in GLS; if `NULL`

, OLS will be
used to estimated fixed effects, and the covariance matrix will be estimated from
the residuals.

verbose

logical defaulting to `TRUE`

-- should updates on progress be printed?

CI.type

Indicates CI type for coefficient functions; options are "pointwise" and
"simultaneous"

## References

Goldsmith, J., Kitago, T. (2016).
Assessing Systematic Effects of Stroke on Motor Control using Hierarchical
Function-on-Scalar Regression. *Journal of the Royal Statistical Society:
Series C*, 65 215-236.