nl_derivatives: Compute first and second derivatives of the fitted spline...

In MultiSpline: Spline-Based Nonlinear Modeling for Multilevel and Longitudinal Data

Compute first and second derivatives of the fitted spline curve

Description

Uses numerical differentiation on the prediction grid to compute the first derivative (slope / marginal effect), the second derivative (curvature), and propagated confidence bands for both, using the delta method from the se.fit column of nl_predict(). Results are passed to nl_turning_points to identify local turning points and inflection regions.

Usage

nl_derivatives(pred_df, x, time = NULL, h = NULL, level = 0.95)

Arguments

pred_df	A data frame returned by nl_predict.
x	Character; name of the focal predictor column.
time	Optional character; name of the time column. If present, derivatives are computed separately within each time level.
h	Numeric; step size for finite-difference approximation. Default NULL uses 0.1 percent of the x range.
level	Confidence level for derivative CIs. Default 0.95.

Value

A data frame with columns x (the focal predictor), time (if applicable), fit (predicted outcome), d1 (first derivative), d1_lwr and d1_upr (lower and upper CI for the first derivative), d2 (second derivative), and d2_lwr and d2_upr (CI for the second derivative).

See Also

nl_turning_points, nl_plot

MultiSpline documentation built on April 16, 2026, 9:06 a.m.