Pcal.fun {DALSM}

Generation of the penalty matrix for an additive model based on P-splines

Description

Compute the penalty matrix associated to a vector containing fixed (non-penalized) parameters and equal-size sub-vectors of penalized B-spline parameters.

Usage

Pcal.fun(nfixed, lambda, Pd.x)

Arguments

nfixed

the number of fixed (i.e. non-penalized) parameters.

lambda

a vector of p penalty parameters where each component is associated to a sub-vector of spline parameters of length J.

Pd.x

a penalty matrix of size J associated to a given sub-vector of spline parameters.

Value

A block diagonal penalty matrix of size (nfixed+pJ) given by Blockdiag(diag(0,nfixed), diag(lambda).kron.Pd.x).

Author(s)

Philippe Lambert [e-mail]

References

Lambert, P. (2021). Fast Bayesian inference using Laplace approximations in nonparametric double additive location-scale models with right- and interval-censored data. Computational Statistics and Data Analysis, 161: 107250. <doi:10.1016/j.csda.2021.107250>

Examples

D = diff(diag(5),diff=2) ## Difference penalty matrix of order 2 for 5 P-spline parameters
P = t(D) %*% D ## Penalty matrix of order 2 for 5 B-spline parameters
lambda = c(100,10) ## Penalty parameters for 2 additive terms with 5 B-spline parameters each
Pcal.fun(3,lambda,P) ## Global penalty matrix for 3 additional non-penalized parameters