splineBasis

Following Wand and Ormerod (2008), compute a low-rank thin plate spline
basis which is diagonalized such that the prior variance for the nonlinear component
is a scalar times a diagonal matrix. Knot locations are determined by quantiles
and the penalty is the integrated squared second derivative.

internal

For Bayesian and classical inference and prediction with count-valued data,
Simultaneous Transformation and Rounding (STAR) Models provide a flexible, interpretable,
and easy-to-use approach. STAR models the observed count data using a rounded
continuous data model and incorporates a transformation for greater flexibility.
Implicitly, STAR formalizes the commonly-applied yet incoherent procedure of
(i) transforming count-valued data and subsequently
(ii) modeling the transformed data using Gaussian models.
STAR is well-defined for count-valued data, which is reflected in predictive accuracy,
and is designed to account for zero-inflation, bounded or censored data, and over- or underdispersion.
Importantly, STAR is easy to combine with existing MCMC or point estimation
methods for continuous data, which allows seamless adaptation of continuous data
models (such as linear regressions, additive models, BART, random forests,
and gradient boosting machines) for count-valued data. The package also includes several
methods for modeling count time series data, namely via warped Dynamic Linear Models.
For more details and background on these methodologies, see the works of
Kowal and Canale (2020) <doi:10.1214/20-EJS1707>,
Kowal and Wu (2022) <doi:10.1111/biom.13617>,
King and Kowal (2022) <arXiv:2110.14790>, and
Kowal and Wu (2023) <arXiv:2110.12316>.

Brian King

countSTAR

Flexible Modeling of Count Data

Dan Kowal

splineBasis function

<dl><dt>tau</dt>
<dd><code>m x 1</code> vector of observed points</dd>
<dt>sumToZero</dt>
<dd>logical; if TRUE, enforce a sum-to-zero constraint (useful for additive models)</dd>
<dt>rescale01</dt>
<dd>logical; if TRUE, rescale <code>tau</code> to the interval [0,1] prior to computing
basis and penalty matrices</dd></dl>

Arguments

Initialize and reparametrize a spline basis matrix — splineBasis

<dl>

<dt>tau</dt>
<dd><code>m x 1</code> vector of observed points</dd>


<dt>sumToZero</dt>
<dd>logical; if TRUE, enforce a sum-to-zero constraint (useful for additive models)</dd>


<dt>rescale01</dt>
<dd>logical; if TRUE, rescale <code>tau</code> to the interval [0,1] prior to computing
basis and penalty matrices</dd>

</dl>

splineBasis: Initialize and reparametrize a spline basis matrix

Description

Usage

Value

Arguments