Consider the data model described in "data":
$$Y_{ij} = \alpha_0(t_{ij})+\sum_{k=1}^{m}\beta_{k}(t_{ij})X_{ijk}+\boldsymbol{Z^\top_{ij}}\boldsymbol{\zeta_{i}}+\epsilon_{ij}.$$
The basis expansion and changing of basis with B splines will be done automatically:
$$\beta_{k}(\cdot)\approx \gamma_{k1} + \sum_{u=2}^{q}{B}_{ku}(\cdot)\gamma_{ku}$$
where \(B_{ku}(\cdot)\) represents B spline basis. \(\gamma_{k1}\) and \((\gamma_{k2}, \ldots, \gamma_{kq})^\top\) correspond to the constant and varying parts of the coefficient functional, respectively.
q=kn+degree+1 is the number of basis functions. By default, kn=degree=2. User can change the values of kn and degree to any other positive integers.
When `structural=TRUE`(default), the coefficient functions with varying effects and constant effects will be penalized separately. Otherwise, the coefficient functions with varying effects and constant effects will be penalized together.
When `sparse="TRUE"` (default), spike-and-slab priors are imposed on individual and/or group levels to identify important constant and varying effects. Otherwise, Laplacian shrinkage will be used.
When `robust=TRUE` (default), the distribution of \(\epsilon_{ij}\) is defined as a Laplace distribution with density.
\(
f(\epsilon_{ij}|\theta,\tau) = \theta(1-\theta)\exp\left\{-\tau\rho_{\theta}(\epsilon_{ij})\right\}
\), (\(i=1,\dots,n,j=1,\dots,J_{i} \)), where \(\theta = 0.5\). If `robust=FALSE`, \(\epsilon_{ij}\) follows a normal distribution.
Please check the references for more details about the prior distributions.