lgspline (version 0.2.0)

take_interaction_2ndderivative: Calculate Second Derivatives of Interaction Terms

Description

Computes partial second derivatives for interaction terms including two-way linear, quadratic, and three-way interactions. Handles special cases for each type.

This function is necessary to compute total second derivatives as the sum of second partial "pure" derivatives (\(d^2/dx^2\)) plus second partial "mixed" derivative (\(d^2/dxdz\)), for a predictor x and all other predictors z.

Usage

take_interaction_2ndderivative(
  dat,
  var,
  interaction_single_cols,
  interaction_quad_cols,
  triplet_cols,
  colnm_expansions,
  power1_cols,
  power2_cols
)

Value

Numeric matrix of second derivatives, same dimensions as input

Arguments

dat

Numeric matrix; design matrix containing basis expansions

var

Character; variable name to differentiate with respect to

interaction_single_cols

Integer vector; column indices for linear-linear interactions

interaction_quad_cols

Integer vector; column indices for linear-quadratic interactions

triplet_cols

Integer vector; column indices for three-way interactions

colnm_expansions

Character vector; column names of expansions for each partition

power1_cols

Integer vector; column indices of linear terms

power2_cols

Integer vector; column indices of quadratic terms