Building Custom Kinetic Models

In rumenGP: Rumen Gas Production Modeling, Comparison, and Visualization

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title: "Building Custom Kinetic Models" output: rmarkdown::html_vignette vignette: > %\VignetteIndexEntry{Building Custom Kinetic Models} %\VignetteEngine{knitr::rmarkdown} \usepackage[utf8]{inputenc}

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knitr::opts_chunk$set(
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Introduction

Most rumen gas production studies rely on a predefined set of kinetic models.

However, researchers often wish to:

• Test novel equations
• Compare alternative model structures
• Develop new biological interpretations
• Reproduce models from the literature

rumenGP provides fit_custom() for fitting user-defined nonlinear kinetic models.

Custom models integrate directly with:

• summary()
• plot_fit()
• plot_residuals()
• compare_models()

This vignette demonstrates how to build, fit, and evaluate custom models.

library(rumenGP)

Example Dataset

Create a simple gas-production dataset.

manual_volume <- data.frame(

  Bottle = c(
    rep(1, 10),
    rep(2, 10)
  ),

  Treatment = c(
    rep("Control", 10),
    rep("Corn", 10)
  ),

  Time = rep(
    c(
      0, 2, 4, 6, 8,
      12, 16, 24, 36, 48
    ),
    2
  ),

  Gas = c(

    0, 5, 12, 20, 28,
    40, 55, 75, 90, 100,

    0, 8, 18, 30, 42,
    58, 72, 95, 110, 120

  )

)

Convert to a rumen_gp object.

gp <- as_rumen_gp(
  data = manual_volume,
  head_col = "Bottle",
  treatment_col = "Treatment",
  time_col = "Time",
  gas_col = "Gas"
)

Example 1: Simple Exponential Model

Consider the equation:

[ Gas(t) = A \left( 1 - e^{-kt} \right) ]

where:

• A = asymptotic gas production
• k = fractional rate constant

Fit the model:

exp_fit <- fit_custom(

  data = gp,

  formula =
    Gas_mL ~
      A *
      (
        1 -
          exp(
            -k * Time_h
          )
      ),

  start = list(
    A = 120,
    k = 0.05
  ),

  lower = c(
    A = 0,
    k = 0
  ),

  model_name =
    "Simple Exponential"

)

Inspect results:

summary(exp_fit)

Estimated parameters:

exp_fit$parameters

Example 2: Hyperbolic Model

Consider:

[ Gas(t) = A \left( \frac{t} { t + K } \right) ]

where:

• A = asymptotic gas production
• K = half-time parameter

Fit the model:

hyperbolic_fit <- fit_custom(

  data = gp,

  formula =
    Gas_mL ~
      A *
      (
        Time_h /
        (
          Time_h + K
        )
      ),

  start = list(
    A = 150,
    K = 10
  ),

  lower = c(
    A = 0,
    K = 0
  ),

  model_name =
    "Hyperbolic"

)

Inspect results:

summary(hyperbolic_fit)

hyperbolic_fit$parameters

Example 3: Richards Model

The Richards model is a flexible four-parameter sigmoidal equation.

[ Gas(t) = VF \left( 1 - b e^{-kt} \right)^m ]

where:

• VF = maximum gas production
• b = interaction constant
• k = fractional rate constant
• m = shape parameter

Fit the model:

richards_fit <- fit_custom(

  data = gp,

  formula =
    Gas_mL ~
      VF *
      (
        1 -
          b *
          exp(
            -k * Time_h
          )
      )^m,

  start = list(
    VF = max(gp$Gas_mL) * 1.1,
    b = 0.9,
    k = 0.05,
    m = 1
  ),

  lower = c(
    VF = 0,
    b = 0,
    k = 0,
    m = 0
  ),

  upper = c(
    VF = Inf,
    b = 1,
    k = Inf,
    m = 10
  ),

  model_name =
    "Richards"

)

Review diagnostics:

richards_fit$diagnostics

Review parameter estimates:

richards_fit$parameters

Comparing Custom and Built-in Models

Custom models can be compared directly with built-in models.

Fit built-in models:

groot_fit <- fit_groot(gp)

brody_fit <- fit_brody(gp)

Compare models:

compare_models(

  Groot = groot_fit,

  Brody = brody_fit,

  Hyperbolic = hyperbolic_fit

)

Visualizing Custom Models

Custom models support the standard visualization workflow.

Plot observed and predicted values:

plot_fit(
  hyperbolic_fit,
  head = 1
)

Plot residuals:

plot_residuals(
  hyperbolic_fit,
  head = 1
)

Choosing Starting Values

Good starting values improve convergence.

Recommendations:

• Set asymptotes slightly above observed maxima
• Use biologically reasonable rate constants
• Start simple before adding parameters

Example:

start = list(
  A = 120,
  k = 0.05
)

Using Bounds

Bounds can prevent unrealistic estimates.

Example:

lower = c(
  A = 0,
  k = 0
)

upper = c(
  A = Inf,
  k = Inf
)

Best Practices

When proposing a new kinetic model:

1. Use biologically meaningful parameters.
2. Choose reasonable starting values.
3. Apply parameter bounds when appropriate.
4. Compare against established models.
5. Evaluate both fit quality and parameter interpretability.

Summary

The fit_custom() framework allows researchers to evaluate new kinetic models without modifying package source code.

Custom models can be:

• fitted,
• visualized,
• compared,
• ranked,

using exactly the same workflow as built-in models.

This makes rumenGP a flexible platform for developing and evaluating novel rumen gas production equations.

rumenGP documentation built on Oct. 2, 2026, 5:09 p.m.