PhotoGEA (version 1.4.0)

confidence_intervals_c4_aci_hyperbola: Calculate confidence intervals for C4 A-Ci hyperbola fitting parameters

Description

Calculates confidence intervals for parameters estimated by a C4 A-Ci curve fit. It is rare for users to call this function directly, because it can be automatically applied to each curve when calling fit_c4_aci_hyperbola.

Usage

confidence_intervals_c4_aci_hyperbola(
    replicate_exdf,
    best_fit_parameters,
    lower = list(),
    upper = list(),
    fit_options = list(),
    sd_A = 1,
    relative_likelihood_threshold = 0.147,
    a_column_name = 'A',
    ci_column_name = 'Ci',
    hard_constraints = 0
  )

Value

An exdf object based on best_fit_parameters that contains lower and upper bounds for each parameter; for example, if Vmax was fit,

best_fit_parameters will contain new columns called Vmax_lower

and Vmax_upper.

Arguments

replicate_exdf

An exdf object representing one CO2 response curve.

best_fit_parameters

An exdf object representing best-fit parameters for the CO2 response curve in replicate_exdf, as calculated by fit_c4_aci_hyperbola.

lower

The same value that was passed to fit_c4_aci_hyperbola when generating best_fit_parameters.

upper

The same value that was passed to fit_c4_aci_hyperbola when generating best_fit_parameters.

fit_options

The same value that was passed to fit_c4_aci_hyperbola when generating best_fit_parameters.

sd_A

The same value that was passed to fit_c4_aci_hyperbola when generating best_fit_parameters.

relative_likelihood_threshold

The threshold value of relative likelihood used to define the boundaries of the confidence intervals; see details below.

a_column_name

The name of the column in replicate_exdf that contains the net assimilation in micromol m^(-2) s^(-1).

ci_column_name

The name of the column in exdf_obj that contains the intercellular CO2 concentration, expressed in micromol mol^(-1).

hard_constraints

To be passed to calculate_c4_assimilation_hyperbola; see that function for more details.

Details

In maximum likelihood fitting, each set of parameter values has an associated likelihood value. If the maximum likelihood is known, then it is also possible to define a relative likelihood p according to p = L / L_max. The set of all parameter values where p exceeds a threshold value p_0 defines a region in parameter space called like a "relative likelihood region." When taking one-dimensional cuts through parameter space, the boundaries of the relative likelihood region define a relative likelihood interval.

Here we calculate the upper and lower limits of the relative likelihood intervals for each parameter. This is done by fixing the other parameters to their best-fit values, and varying a single parameter to find the interval where the relative likelihood is above the threshold value (set by the relative_likelihood_threshold input argument). If the threshold is set to 0.147, then these intervals are equivalent to 95% confidence intervals in most situations. See the Wikipedia page about relative likelihood for more information.

Internally, this function uses error_function_c4_aci_hyperbola to calculate the negative logarithm of the likelihood (-ln(L)). It varies each fitting parameter independendently to find values where ln(L) - ln(p_0) - ln(L_max) = 0.

If the upper limit of a confidence interval is found to exceed ten times the upper limit specified when fitting that parameter, then the upper limit of the condfidence interval is taken to be infinity.

Examples

# Read an example Licor file included in the PhotoGEA package
licor_file <- read_gasex_file(
  PhotoGEA_example_file_path('c4_aci_1.xlsx')
)

# Define a new column that uniquely identifies each curve
licor_file[, 'species_plot'] <-
  paste(licor_file[, 'species'], '-', licor_file[, 'plot'] )

# Organize the data
licor_file <- organize_response_curve_data(
    licor_file,
    'species_plot',
    c(9, 10, 16),
    'CO2_r_sp'
)

# Fit just one curve from the data set
one_result <- fit_c4_aci_hyperbola(
  licor_file[licor_file[, 'species_plot'] == 'maize - 5', , TRUE],
  calculate_confidence_intervals = FALSE
)

# Calculate confidence limits for the fit parameters
parameters_with_limits <- confidence_intervals_c4_aci_hyperbola(
    licor_file[licor_file[, 'species_plot'] == 'maize - 5', , TRUE],
    one_result$parameters
)

# View confidence limits and best estimate for Vmax
parameters_with_limits[, c('Vmax_lower', 'Vmax', 'Vmax_upper')]