equation: Print Closed-Form Fitted Equation from lgspline Model

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Print Closed-Form Fitted Equation from lgspline Model

Description

Displays the closed-form polynomial equation for each partition of a fitted lgspline model, along with partition boundary or cluster center information. Optionally prints the first derivative, second derivative, or antiderivative of the fitted equation with respect to a single specified variable.

Usage

equation(object, ...)

## S3 method for class 'lgspline'
equation(
  object,
  digits = 4,
  scientific = FALSE,
  show_bounds = TRUE,
  predictor_names = NULL,
  response_name = NULL,
  collapse_zero = TRUE,
  first_derivative = NULL,
  second_derivative = NULL,
  antiderivative = NULL,
  ...
)

## S3 method for class 'equation'
print(x, ...)

## S3 method for class 'lgspline'
equation(
  object,
  digits = 4,
  scientific = FALSE,
  show_bounds = TRUE,
  predictor_names = NULL,
  response_name = NULL,
  collapse_zero = TRUE,
  first_derivative = NULL,
  second_derivative = NULL,
  antiderivative = NULL,
  ...
)

## S3 method for class 'equation'
print(x, ...)

Arguments

object	A fitted lgspline model object.
...	Not used.
digits	Integer; decimal places for coefficient display. Default 4.
scientific	Logical; use scientific notation for coefficients with absolute value < 1e-3 or > 1e4. Default FALSE.
show_bounds	Logical; display partition bounds (1D) or knot midpoint boundaries (multi-D). Default TRUE.
predictor_names	Character vector; custom names for predictor variables. If NULL (default), uses original column names or "_j_" labels.
response_name	Character; label for response. If NULL (default), uses "y" for identity link Gaussian, or "link(E[y])" otherwise.
collapse_zero	Logical; omit terms with coefficient exactly 0. Default TRUE.
first_derivative	Default: NULL. Character name or integer index of the predictor variable with respect to which the first derivative is printed. Only one variable at a time is supported. When non-NULL, the printed equations show df/dx_j for each partition.
second_derivative	Default: NULL. Character name or integer index of the predictor variable with respect to which the second derivative is printed. Only one variable at a time is supported. When non-NULL, the printed equations show d^2f/dx_j^2 for each partition. Ignored if first_derivative is also non-NULL.
antiderivative	Default: NULL. Character name or integer index of the predictor variable with respect to which the antiderivative (indefinite integral) is printed. Only one variable at a time is supported. When non-NULL, the printed equations show \int f\, dx_j for each partition, with an unspecified constant of integration C. Ignored if first_derivative or second_derivative is also non-NULL.
x	An object returned by equation() for printing.

Details

For 1D models with K knots, partition boundaries are displayed as intervals on the predictor scale. For multi-predictor models, partition boundaries are computed as the midpoints between adjacent cluster centers along each predictor dimension. When the model's make_partition_list contains knots (midpoint boundaries between clusters), those are used directly. Otherwise, cluster centers are displayed.

Coefficients are displayed on the original (unstandardized) predictor scale. For GLMs with non-identity link, the left-hand side shows the link function applied to the expected response.

Derivative and antiderivative modes. Only one of first_derivative, second_derivative, or antiderivative may be non-NULL. If more than one is supplied, the priority order is: first derivative, second derivative, antiderivative.

Derivatives and antiderivatives are computed symbolically from the polynomial coefficients. For a term a x^n, the first derivative is n a x^{n-1}, the second derivative is n(n-1) a x^{n-2}, and the antiderivative is a x^{n+1}/(n+1). Cross-terms (interactions) involving the target variable are differentiated or integrated with respect to that variable only, treating all other variables as constants.

A warning is emitted if the user attempts to differentiate or integrate with respect to more than one variable simultaneously. Multi-variable calculus operations should be performed one variable at a time by calling equation() repeatedly.

Value

Invisibly returns a list with components:

formulas

Character vector of equation strings per partition.

bounds

Matrix or list of partition boundary information.

link

Character; link function name.

mode

Character; one of "equation", "first_derivative", "second_derivative", or "antiderivative".

variable

Character; the variable name for the calculus operation, or NULL if mode is "equation".

See Also

lgspline, plot.lgspline, coef.lgspline

Examples

## 1D example
set.seed(1234)
t <- runif(500, -5, 5)
y <- 2*sin(t) + 0.1*t^2 + rnorm(length(t), 0, 0.5)
fit <- lgspline(t, y, K = 2)
equation(fit)
equation(fit, digits = 2, predictor_names = "time")

## First derivative with respect to predictor
equation(fit, first_derivative = 1)

## Second derivative
equation(fit, second_derivative = 1)

## Antiderivative
equation(fit, antiderivative = 1)

## 2D example with named predictors
x1 <- runif(300, 0, 10)
x2 <- runif(300, 0, 10)
y <- x1 + 0.5*x2 + 0.1*x1*x2 + rnorm(300)
fit2d <- lgspline(cbind(x1, x2), y, K = 3)
equation(fit2d, predictor_names = c("Length", "Width"))

## Derivative w.r.t. first variable only
equation(fit2d, first_derivative = "Length",
         predictor_names = c("Length", "Width"))

## GLM example
y_bin <- rbinom(500, 1, plogis(0.5*t))
fit_glm <- lgspline(t, y_bin, family = binomial(), K = 1)
equation(fit_glm)

lgspline documentation built on May 8, 2026, 5:07 p.m.