Finds initial smoothing parameter guesses for multiple smoothing
parameter estimation. The idea is to find values such that the estimated
degrees of freedom per penalized parameter should be well away from 0 and 1
for each penalized parameter, thus ensuring that the values are in a region of
parameter space where the smoothing parameter estimation criterion is varying
substantially with smoothing parameter value.

initial.sp

Generalized additive (mixed) models, some of their extensions and
other generalized ridge regression with multiple smoothing
parameter estimation by (Restricted) Marginal Likelihood,
Cross Validation and similar, or using iterated nested Laplace
approximation for fully Bayesian inference. See Wood (2025)
<doi:10.1146/annurev-statistics-112723-034249> for an overview.
Includes a gam() function, a wide variety of smoothers, 'JAGS'
support and distributions beyond the exponential family.

Simon Wood

mgcv

Mixed GAM Computation Vehicle with Automatic Smoothness
Estimation

initial.sp function

Starting values for multiple smoothing parameter estimation — initial.sp

<dl>


<dt>X</dt>
<dd>is the model matrix.</dd>


<dt>S</dt>
<dd>is a list of of penalty matrices. <code>S[[i]]</code> is the ith penalty matrix, but note
that it is not stored as a full matrix, but rather as the smallest square matrix including all 
the non-zero elements of the penalty matrix. Element 1,1 of <code>S[[i]]</code> occupies 
element <code>off[i]</code>, <code>off[i]</code> of the ith penalty matrix. Each <code>S[[i]]</code> must be 
positive semi-definite.</dd>


<dt>off</dt>
<dd>is an array indicating the first parameter in the parameter vector that is 
penalized by the penalty involving <code>S[[i]]</code>.</dd>


<dt>expensive</dt>
<dd>if <code>TRUE</code> then the overall amount of smoothing is
adjusted so that the average degrees of freedom per penalized parameter is
exactly 0.5: this is numerically costly.</dd>


<dt>XX</dt>
<dd>if <code>TRUE</code> then <code>X</code> contains \(X^TX\), rather than \(X\).</dd>

</dl>

Arguments

Simon N. Wood <a href='mailto:simon.wood@r-project.org'>simon.wood@r-project.org</a>

initial.sp: Starting values for multiple smoothing parameter estimation

Description

Usage

Arguments

Value

Details

See Also