take_derivative

Computes first or second derivatives of polynomial terms in a design matrix with
respect to a specified variable. Handles polynomial terms up to fourth degree.

internal

Implements Lagrangian multiplier smoothing splines for flexible
nonparametric regression and function estimation. Provides tools for fitting,
prediction, and inference using a constrained optimization approach to
enforce smoothness.
Supports generalized linear models, Weibull accelerated failure time (AFT) models,
quadratic programming problems, and customizable arbitrary correlation structures.
Options for fitting in parallel are provided. The method builds upon the framework described
by Ezhov et al. (2018) <doi:10.1515/jag-2017-0029> using Lagrangian multipliers
to fit cubic splines. For more information on correlation structure estimation,
see Searle et al. (2009) <ISBN:978-0470009598>. For quadratic programming and
constrained optimization in general, see Nocedal & Wright (2006) <doi:10.1007/978-0-387-40065-5>.
For a comprehensive background on smoothing splines, see Wahba (1990)
<doi:10.1137/1.9781611970128> and Wood (2006) <ISBN:978-1584884743>
"Generalized Additive Models: An Introduction with R".

Matthew Davis

lgspline

Lagrangian Multiplier Smoothing Splines for Smooth Function
Estimation

take_derivative function

<dl><dt>dat</dt>
<dd>Numeric matrix; design matrix containing polynomial basis expansions</dd>
<dt>var</dt>
<dd>Character; column name of variable to differentiate with respect to</dd>
<dt>second</dt>
<dd>Logical; if TRUE compute second derivative, if FALSE compute first derivative (default FALSE)</dd>
<dt>scale</dt>
<dd>Numeric; scaling factor for normalization</dd></dl>

Arguments

Calculate Derivatives of Polynomial Terms — take_derivative

<dl>

<dt>dat</dt>
<dd>Numeric matrix; design matrix containing polynomial basis expansions</dd>


<dt>var</dt>
<dd>Character; column name of variable to differentiate with respect to</dd>


<dt>second</dt>
<dd>Logical; if TRUE compute second derivative, if FALSE compute first derivative (default FALSE)</dd>


<dt>scale</dt>
<dd>Numeric; scaling factor for normalization</dd>

</dl>

take_derivative: Calculate Derivatives of Polynomial Terms

Description

Usage

Value

Arguments