Sp {bage}R Documentation

P-Spline Prior

Description

Use a p-spline (penalised spline) to model main effects or interactions. Typically used with age, but can be used with any variable where outcomes are expected to vary smoothly from one element to the next.

Usage

Sp(
  n_comp = NULL,
  s = 1,
  sd = 1,
  sd_slope = 1,
  along = NULL,
  con = c("none", "by")
)

Arguments

n_comp

Number of spline basis functions (components) to use.

s

Scale for the prior for the innovations. Default is 1.

sd

Standard deviation in prior for first element of random walk.

sd_slope

Standard deviation in prior for initial slope of random walk. Default is 1.

along

Name of the variable to be used as the 'along' variable. Only used with interactions.

con

Constraints on parameters. Current choices are "none" and "by". Default is "none". See below for details.

Details

If Sp() is used with an interaction, separate splines are used for the 'along' variable within each combination of the 'by' variables.

Value

An object of class "bage_prior_spline".

Mathematical details

When Sp() is used with a main effect,

\pmb{\beta} = \pmb{X} \pmb{\alpha}

and when it is used with an interaction,

\pmb{\beta}_u = \pmb{X} \pmb{\alpha}_u

where

The elements of \pmb{\alpha} or \pmb{\alpha}_u are assumed to follow a second-order random walk.

Constraints

With some combinations of terms and priors, the values of the intercept, main effects, and interactions are are only weakly identified. For instance, it may be possible to increase the value of the intercept and reduce the value of the remaining terms in the model with no effect on predicted rates and only a tiny effect on prior probabilities. This weak identifiability is typically harmless. However, in some applications, such as when trying to obtain interpretable values for main effects and interactions, it can be helpful to increase identifiability through the use of constraints, specified through the con argument.

Current options for con are:

References

See Also

Examples

Sp()
Sp(n_comp = 10)

[Package bage version 0.9.4 Index]