Fit Logistic-Exponential model (LE0)

Fits the Logistic-Exponential model without an explicit lag phase.

Usage

fit_le0(data, start = NULL)

Arguments

data

A rumen_gp object.

start

Optional list of starting values. May contain any of:

• A

• k

• d

Value

A le0_fit object containing:

• Parameter estimates

• Model diagnostics

• Predicted values

• Residuals

Details

Equation

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

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

Interpretation

The LE0 model combines an exponential fermentation component with a logistic component.

Compared with simple exponential models, LE0 provides additional flexibility in curve shape without requiring an explicit lag parameter.

Advantages

• Flexible sigmoidal behavior

• More adaptable than simple exponential models

• No lag parameter required

• Can accommodate gradual changes in fermentation rate

Limitations

• More complex than EXP0

• Shape parameter may be less intuitive biologically

• Additional parameter may increase parameter correlation

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_le0(
  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 (LE0) 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_le0(
  gp,
  start = list(
    A = 120,
    k = 0.05,
    d = 0.50
  )
)
#> 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 (LE0) model summary
#> ----------------------------------------
#> Total bottles: 24
#> Successful fits: 24
#> Failed fits: 0
#> Low R-squared (< 0.90): 3
#>