make_derivative_matrix

Compute First and Second Derivative Matrices

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

make_derivative_matrix function

<dl><dt>nc</dt>
<dd>Number of columns</dd>
<dt>Cpredictors</dt>
<dd>Predictor matrix</dd>
<dt>power1_cols</dt>
<dd>Indices of linear terms of spline effects</dd>
<dt>power2_cols</dt>
<dd>Indices of quadratic terms of spline effects</dd>
<dt>nonspline_cols</dt>
<dd>Indices of non-spline effects</dd>
<dt>interaction_single_cols</dt>
<dd>Indices of first-order interactions</dd>
<dt>interaction_quad_cols</dt>
<dd>Indices of quadratic interactions</dd>
<dt>triplet_cols</dt>
<dd>Indices of three-way interactions</dd>
<dt>K</dt>
<dd>Number of partitions minus 1 (\(K\))</dd>
<dt>include_2way_interactions</dt>
<dd>Include 2-way interactions</dd>
<dt>include_3way_interactions</dt>
<dd>Include 3-way interactions</dd>
<dt>include_quadratic_interactions</dt>
<dd>Include quadratic interactions</dd>
<dt>colnm_expansions</dt>
<dd>Column names</dd>
<dt>expansion_scales</dt>
<dd>Scale factors</dd>
<dt>just_first_derivatives</dt>
<dd>Only compute first derivatives</dd>
<dt>just_spline_effects</dt>
<dd>Only compute derivatives for spline effects</dd></dl>

Arguments

Compute First and Second Derivative Matrices — make_derivative_matrix

<dl>

<dt>nc</dt>
<dd>Number of columns</dd>


<dt>Cpredictors</dt>
<dd>Predictor matrix</dd>


<dt>power1_cols</dt>
<dd>Indices of linear terms of spline effects</dd>


<dt>power2_cols</dt>
<dd>Indices of quadratic terms of spline effects</dd>


<dt>nonspline_cols</dt>
<dd>Indices of non-spline effects</dd>


<dt>interaction_single_cols</dt>
<dd>Indices of first-order interactions</dd>


<dt>interaction_quad_cols</dt>
<dd>Indices of quadratic interactions</dd>


<dt>triplet_cols</dt>
<dd>Indices of three-way interactions</dd>


<dt>K</dt>
<dd>Number of partitions minus 1 (\(K\))</dd>


<dt>include_2way_interactions</dt>
<dd>Include 2-way interactions</dd>


<dt>include_3way_interactions</dt>
<dd>Include 3-way interactions</dd>


<dt>include_quadratic_interactions</dt>
<dd>Include quadratic interactions</dd>


<dt>colnm_expansions</dt>
<dd>Column names</dd>


<dt>expansion_scales</dt>
<dd>Scale factors</dd>


<dt>just_first_derivatives</dt>
<dd>Only compute first derivatives</dd>


<dt>just_spline_effects</dt>
<dd>Only compute derivatives for spline effects</dd>

</dl>

make_derivative_matrix: Compute First and Second Derivative Matrices

Description

Usage

Value

Arguments