fit_mm: Fit Michaelis-Menten model

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

Fit Michaelis-Menten model

Description

Fits the generalized Michaelis-Menten model to each bottle in a rumen_gp dataset.

Usage

fit_mm(data, start = NULL)

Arguments

data	A rumen_gp object.
start	Optional list of starting values. May contain any of: A K c

Details

Equation

V(t) = A \frac{t^{c}} { t^{c}+K^{c} }

where:

• V(t) is cumulative gas production at time t

• A is asymptotic gas production

• K is the half-time parameter

• c is the shape parameter

Interpretation

The generalized Michaelis-Menten model describes cumulative gas production using a flexible sigmoidal function.

The parameter K represents the time required to reach approximately half of the asymptotic gas production, while c controls curve shape and steepness.

Advantages

• Flexible sigmoidal behavior

• Biologically meaningful half-time parameter

• Usually converges reliably

• Well suited for rumen gas production data

Limitations

• Shape parameter may be difficult to interpret biologically

• More complex than simple exponential models

Notes

The generalized Michaelis-Menten model is mathematically equivalent to the Groot model implemented in fit_groot().

Parameter correspondence:

• A = VF

• K = b

• c = k

Both formulations produce identical fitted values and model diagnostics when convergence is achieved.

Researchers may choose either formulation according to the terminology commonly used in their field.

Value

A mm_fit object containing:

• Parameter estimates

• Model diagnostics

• Predicted values

• Residuals

Examples

files <- example_data()

raw_data <- read_ankom(
  files$ankom
)

metadata <- read_metadata(
  files$metadata
)

gp <- process_ankom(
  raw_data,
  metadata,
  headspace_ml = 210,
  temperature_c = 39
)

# Fit using package default starting values
fit_default <- fit_mm(
  gp
)

summary(fit_default)

# Fit using custom starting values
fit_custom_start <- fit_mm(
  gp,
  start = list(
    A = 120,
    K = 10,
    c = 2
  )
)

summary(fit_custom_start)

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