Calculate confidence intervals for C4 A-Ci hyperbola fitting parameters
confidence_intervals_c4_aci_hyperbola.Rd
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
.
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 inreplicate_exdf
, as calculated byfit_c4_aci_hyperbola
.- lower
The same value that was passed to
fit_c4_aci_hyperbola
when generatingbest_fit_parameters
.- upper
The same value that was passed to
fit_c4_aci_hyperbola
when generatingbest_fit_parameters
.- fit_options
The same value that was passed to
fit_c4_aci_hyperbola
when generatingbest_fit_parameters
.- sd_A
The same value that was passed to
fit_c4_aci_hyperbola
when generatingbest_fit_parameters
.- error_threshold_factor
A multiplicative factor that sets the threshold value of the error function used to define the edges of the confidence intervals; see details below.
- a_column_name
The name of the column in
replicate_exdf
that contains the net assimilation inmicromol m^(-2) s^(-1)
.- ci_column_name
The name of the column in
exdf_obj
that contains the intercellular CO2 concentration, expressed inmicromol 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. If the threshold
p_0
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.
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.
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
.
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 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')]
#> Vmax_lower Vmax Vmax_upper
#> 1 64.21675 65.12738 66.04023