Fit Logistic-Exponential model (LEL)

Fits the Logistic-Exponential model with an explicit lag phase.

Usage

fit_lel(data, start = NULL)

Arguments

data

A rumen_gp object.

start

Optional list of starting values. May contain any of:

• A

• k

• d

• lambda

Value

A lel_fit object containing:

• Parameter estimates

• Model diagnostics

• Predicted values

• Residuals

Details

Equation

$$ V(t) = \frac{ A \left( 1-e^{-k(t-\lambda)} \right) } { 1+\exp \left[ \ln\left(\frac{1}{d}\right) - k(t-\lambda) \right] } $$

where:

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

• \(A\) is asymptotic gas production

• \(k\) is the fractional rate constant

• \(d\) is a shape parameter

• \(\lambda\) is lag time

Interpretation

The LEL model combines an exponential fermentation component, a logistic component, and an explicit lag phase.

This model is more flexible than traditional exponential models and can describe complex fermentation dynamics with delayed onset of gas production.

Advantages

• Explicit lag parameter

• Flexible sigmoidal behavior

• Can represent delayed fermentation

• Often fits complex gas production profiles well

Limitations

• More parameters than EXP0 or EXPL

• Greater risk of parameter correlation

• May require careful starting values

• Increased computational complexity

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_lel(
  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-Exponential (LEL) model summary
#> ----------------------------------------
#> Total bottles: 24
#> Successful fits: 23
#> Failed fits: 1
#> Low R-squared (< 0.90): 11
#> Lambda at boundary: 11
#> 

# Fit using custom starting values
fit_custom_start <- fit_lel(
  gp,
  start = list(
    A = 120,
    k = 0.05,
    d = 0.50,
    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-Exponential (LEL) model summary
#> ----------------------------------------
#> Total bottles: 24
#> Successful fits: 24
#> Failed fits: 0
#> Low R-squared (< 0.90): 13
#> Lambda at boundary: 12
#>