dot-smooth.spec: Basis constructor for PEER terms

In refund: Regression with Functional Data

Basis constructor for PEER terms

Description

Smooth basis constructor to define structured penalties (Randolph et al., 2012) for smooth terms.

Usage

.smooth.spec(object, data, knots)

Arguments

object	a peer.smooth.spec object, usually generated by a term s(x, bs="peer"); see Details.
data	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.
knots	not used, but required by the generic smooth.construct.

Details

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:

1. xt$pentype=="RIDGE" for a ridge penalty, the default

2. xt$pentype=="D" for a difference penalty. The order of the difference penalty is specified by the m argument of s().

3. 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.

4. xt$pentype=="USER" for a user-specified penalty matrix L, supplied by xt$L.

Value

An object of class "peer.smooth". See {smooth.construct} for the elements that this object will contain.

Author(s)

Madan Gopal Kundu [e-mail] and Jonathan Gellar

References

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.

See Also

{peer}

refund documentation built on Sept. 21, 2024, 1:07 a.m.