Fit Logistic model

Fits a Logistic gas-production model to each bottle in a rumen_gp dataset.

Usage

fit_logistic(data, start = NULL)

Arguments

data

A rumen_gp object.

start

Optional list of starting values. May contain any of:

• A

• k

• lambda

Value

A logistic_fit object containing:

• Parameter estimates

• Model diagnostics

• Predicted values

• Residuals

Details

Equation

$$ V(t) = \frac{A} { 1+\exp \left[ 2+ 4k(\lambda-t) \right] } $$

where:

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

• \(A\) is asymptotic gas production

• \(k\) is the fractional rate constant

• \(\lambda\) is lag time

Interpretation

The Logistic model describes gas production using a sigmoidal curve with an initial lag phase, a period of rapid fermentation, and a plateau approaching the asymptotic gas production.

The parameter \(k\) controls the steepness of the curve, while \(\lambda\) determines the position of the sigmoid along the time axis.

Advantages

• Explicit lag parameter

• Smooth sigmoidal behavior

• Stable convergence

• Widely used in biological growth and fermentation studies

Limitations

• Assumes a symmetric sigmoidal curve

• May not adequately fit highly asymmetric fermentation profiles

• Less flexible than Gompertz or Dual Logistic models

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_logistic(
  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)
#> 
#> Logistic model summary
#> ----------------------
#> Total bottles: 24
#> Successful fits: 24
#> Failed fits: 0
#> Low R-squared (< 0.90): 7
#> Lambda at boundary: 9
#> 

# Fit using custom starting values
fit_custom_start <- fit_logistic(
  gp,
  start = list(
    A = 120,
    k = 0.05,
    lambda = 1
  )
)
#> 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)
#> 
#> Logistic model summary
#> ----------------------
#> Total bottles: 24
#> Successful fits: 23
#> Failed fits: 1
#> Low R-squared (< 0.90): 12
#> Lambda at boundary: 12
#>