Fit Michaelis-Menten model — fit

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:

Value

A mm_fit object containing:

Parameter estimates
Model diagnostics
Predicted values
Residuals

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.

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
)
#> Warning: Large negative pressure values detected. Minimum PSI = -1.274 . Please inspect the affected bottles.
#> rumenGP data validation passed.
#> Observations: 1752
#> Heads: 24
#> Treatments: 5

summary(fit_default)
#> 
#> Michaelis-Menten model summary
#> ------------------------------
#> Total bottles: 24
#> Successful fits: 23
#> Failed fits: 1
#> Low R-squared (< 0.90): 2
#> 

# Fit using custom starting values
fit_custom_start <- fit_mm(
  gp,
  start = list(
    A = 120,
    K = 10,
    c = 2
  )
)
#> Warning: Large negative pressure values detected. Minimum PSI = -1.274 . Please inspect the affected bottles.
#> rumenGP data validation passed.
#> Observations: 1752
#> Heads: 24
#> Treatments: 5

summary(fit_custom_start)
#> 
#> Michaelis-Menten model summary
#> ------------------------------
#> Total bottles: 24
#> Successful fits: 24
#> Failed fits: 0
#> Low R-squared (< 0.90): 3
#>