Fit Mitscherlich model

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

Usage

fit_mitscherlich(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 mitscherlich_fit object containing:

• Parameter estimates

• Model diagnostics

• Predicted values

• Residuals

Details

Equation

$$ V(t) = A \left[ 1 - \exp \left( -k(t-\lambda) - d \left( \sqrt{t+0.001} - \sqrt{\lambda+0.001} \right) \right) \right] $$

where:

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

• \(A\) is asymptotic gas production

• \(k\) is the fractional rate constant

• \(d\) is a diffusion or shape parameter

• \(\lambda\) is lag time

Interpretation

The Mitscherlich model combines an exponential fermentation component with a diffusion-like term.

The parameter \(k\) describes the primary fermentation rate, while \(d\) provides additional flexibility for representing changes in fermentation dynamics over time.

Advantages

• Explicit lag parameter

• Flexible curve shape

• Can describe complex fermentation dynamics

• Often performs well when simple exponential models are inadequate

Limitations

• More complex than EXP0 or EXPL

• Increased parameter correlation

• Diffusion parameter may be less intuitive biologically

• May require careful starting values

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_mitscherlich(
  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)
#> 
#> Mitscherlich model summary
#> ---------------------------
#> Total bottles: 24
#> Successful fits: 23
#> Failed fits: 1
#> Low R-squared (< 0.90): 3
#> Lambda at boundary: 2
#> 

# Fit using custom starting values
fit_custom_start <- fit_mitscherlich(
  gp,
  start = list(
    A = 120,
    k = 0.05,
    d = 0.05,
    lambda = 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)
#> 
#> Mitscherlich model summary
#> ---------------------------
#> Total bottles: 24
#> Successful fits: 24
#> Failed fits: 0
#> Low R-squared (< 0.90): 4
#> Lambda at boundary: 2
#>