Fit exponential model with lag (EXPL) — fit

Fits the exponential gas production model with an explicit lag phase.

Usage

fit_expl(data, start = NULL)

Arguments

data

A rumen_gp object.

start

Optional list of starting values. May contain any of:

Vf
k
lambda

Value

An expl_fit object containing:

Parameter estimates
Model diagnostics
Predicted values
Residuals

Details

Equation

$$ V(t) = Vf \left(1 - e^{-k(t-\lambda)}\right) $$

where:

$V(t)$ is cumulative gas production at time $t$
$Vf$ is asymptotic gas production
$k$ is the fractional rate constant
$\lambda$ is lag time

Interpretation

The EXPL model assumes that gas production follows an exponential pattern after a lag phase. The lag parameter represents the delay before substantial fermentation begins.

Advantages

Explicit lag parameter
Simple biological interpretation
Stable convergence

Limitations

Less flexible than sigmoidal models
May not adequately represent multiple fermentation phases

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_expl(
  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)
#> 
#> Exponential model with lag (EXPL) summary
#> -----------------------------------------
#> Total bottles: 24
#> Successful fits: 23
#> Failed fits: 1
#> Low R-squared (< 0.90): 3
#> Lambda at boundary: 8
#> 

# Fit using custom starting values
fit_custom_start <- fit_expl(
  gp,
  start = list(
    Vf = 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)
#> 
#> Exponential model with lag (EXPL) summary
#> -----------------------------------------
#> Total bottles: 24
#> Successful fits: 24
#> Failed fits: 0
#> Low R-squared (< 0.90): 6
#> Lambda at boundary: 8
#>