Fitting function for function-on-scalar regression for cross-sectional data. This function estimates model parameters using a Gibbs sampler and estimates the residual covariance surface using FPCA.

```
gibbs_cs_fpca(
formula,
Kt = 5,
Kp = 2,
data = NULL,
verbose = TRUE,
N.iter = 5000,
N.burn = 1000,
SEED = NULL,
sig2.me = 0.01,
alpha = 0.1,
Aw = NULL,
Bw = NULL,
Apsi = NULL,
Bpsi = NULL
)
```

formula

a formula indicating the structure of the proposed model.

Kt

number of spline basis functions used to estimate coefficient functions

Kp

number of FPCA basis functions to be estimated

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.

verbose

logical defaulting to `TRUE`

-- should updates on progress be printed?

N.iter

number of iterations used in the Gibbs sampler

N.burn

number of iterations discarded as burn-in

SEED

seed value to start the sampler; ensures reproducibility

sig2.me

starting value for measurement error variance

alpha

tuning parameter balancing second-derivative penalty and zeroth-derivative penalty (alpha = 0 is all second-derivative penalty)

Aw

hyperparameter for inverse gamma controlling variance of spline terms for population-level effects

Bw

hyperparameter for inverse gamma controlling variance of spline terms for population-level effects

Apsi

hyperparameter for inverse gamma controlling variance of spline terms for FPC effects

Bpsi

hyperparameter for inverse gamma controlling variance of spline terms for FPC effects

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.