This function generates penalty matrices for the two dimensions of predictor and lags, given the functions selected to model the relationship in each space. It can also be used for generating the single penalty matrix for the predictor space of a uni-dimensional basis not accouning for lags.
cbPen(cb, sp=-1, addSlag=NULL)an object of class "crossbasis" or "onebasis".
supplied smoothing parameters. See Details below.
matrix or vector (or list of matrices and/or vectors) defining additional penalties on the lag structure. See Details below.
A list including penalty matrices plus two vectors rank and sp defining their rank and the smoothing parameters. This list is consistent with the argument paraPen in the regression function gam function of mgcv.
This function is used to perform penalized regression models using the external method. This involves generating the transformation using crossbasis or onebasis with functions for penalized splines (either ps or cr). The function cbPen is then called to generate a list of the related penalty matrices. The model is performed by penalizing so-called parametric terms in the gam function of mgcv, by including the basis or cross-basis matrix in the regression formula and the list of penalty matrices in its paraPen argument.
When cb is a cross-basis object, the penalty matrices for the two spaces of predictor and lags are rescaled and expanded accordingly to its tensor product-type structure. A penalty matrix is not defined when using a function different than ps or cr, thus keeping one of the two dimensions unpenalized.
Additional penalties on the lag dimension can be added through the argument addSlag, either as a single matrix or a list of matrices. If provided as a vector, this is taken as the diagonal of the penalty matrix and expanded accordingly. These objects must have appropriate dimensions in accordance with the basis matrix for the lag space.
All the penalty matrices are also appropriately rescaled to improve the estimation process.
The vector sp must have the same length as the number of penalties, including additional penalties on the lags, and it is replicated accordingly if of length 1. Positive or zero elements are taken as fixed smoothing parameters. Negative elements signal that these parameters need to be estimated.
Gasparrini A, Scheipl F, Armstrong B, Kenward MG. A penalized framework for distributed lag non-linear models. Biometrics. 2017;73(3):938-948. [freely available here]
Wood S. N. Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC Press, 2006.
ps and cr for penalized spline functions. The cb smooth constructor for cross-basis penalized spline smooths.
See dlnm-package for an introduction to the package and for links to package vignettes providing more detailed information, in particular the vignette dlnmPenalized.
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