Smooth basis constructor to define structured penalties (Randolph et al., 2012) for smooth terms.
# S3 method for peer.smooth.spec
smooth.construct(object, data, knots)a peer.smooth.spec object, usually generated by a
term s(x, bs="peer"); see Details.
a list containing the data (including any by variable)
required by this term, with names corresponding to object$term
(and object$by). Only the first element of this list is used.
not used, but required by the generic smooth.construct.
An object of class "peer.smooth". See
smooth.construct for the elements that this object will
contain.
The smooth specification object, defined using s(), should
contain an xt element. xt will be a list that contains
additional information needed to specify the penalty. The type of penalty
is indicated by xt$pentype. There are four types of penalties
available:
xt$pentype=="RIDGE" for a ridge penalty, the default
xt$pentype=="D" for a difference penalty. The order of the
difference penalty is specified by the m argument of
s().
xt$pentype=="DECOMP" for a decomposition-based penalty,
\(bP_Q + a(I-P_Q)\), where \(P_Q = Q^t(QQ^t)^{-1}Q\). The \(Q\)
matrix must be specified by xt$Q, and the scalar \(a\) by
xt$phia. The number of columns of Q must be equal to the
length of the data. Each row represents a basis function where the
functional predictor is expected to lie, according to prior belief.
xt$pentype=="USER" for a user-specified penalty matrix
\(L\), supplied by xt$L.
Randolph, T. W., Harezlak, J, and Feng, Z. (2012). Structured penalties for functional linear models - partially empirical eigenvectors for regression. Electronic Journal of Statistics, 6, 323-353.