Calculate Mohn's rho for retrospective analysis

Calculates Mohn's rho, a diagnostic statistic that summarizes the bias in retrospective analysis. The statistic measures the average relative difference between estimates from retrospective peels and the reference model at the corresponding terminal year of each peel. A value close to zero suggests minimal retrospective bias, while larger absolute values indicate potential model misspecification or data conflicts.

The formula for Mohn's rho is: $$\rho = \frac{1}{n} \sum_{i=1}^{n} \frac{x_{peel,i} - x_{base,i}}{x_{base,i}}$$ where n is the number of retrospective peels, \(x_{peel,i}\) is the estimated value from peel i at its terminal year, and \(x_{base,i}\) is the value from the base model at that same year.

Usage

calculate_mohns_rho(retro_fit, quantity)

Arguments

retro_fit

List returned by the run_fims_retrospective() function containing years_to_remove (vector of years peeled) and estimates (data frame with retrospective results)

quantity

Character string specifying which quantity to calculate Mohn's rho for (e.g., "spawning_biomass", "expected_recruitment")

Value

A numeric value representing Mohn's rho. Values close to zero indicate minimal retrospective bias. Positive values suggest the model retrospectively underestimates the quantity, while negative values suggest overestimation.

Details

Calculate Mohn's rho for retrospective analysis

References

Mohn, R. (1999). The retrospective problem in sequential population analysis: An investigation using cod fishery and simulated data. ICES Journal of Marine Science, 56(4), 473-488.

Hurtado-Ferro, F., Szuwalski, C.S., Valero, J.L., Anderson, S.C., Cunningham, C.J., Johnson, K.F., Licandeo, R., McGilliard, C.R., Monnahan, C.C., Muradian, M.L., Ono, K., Vert-Pre, K.A., Whitten, A.R., and Punt, A.E. (2015). Looking in the rear-view mirror: bias and retrospective patterns in integrated, age-structured stock assessment models. ICES Journal of Marine Science, 72(1), 99-110.

Examples

if (FALSE) { # \dontrun{
library(FIMS)
# Use built-in dataset from FIMS
data("data1")
# Prepare data for FIMS model
data_4_model <- FIMSFrame(data1)
# Create parameters
parameters <- data_4_model |>
  create_default_configurations() |>
  create_default_parameters(data = data_4_model)

# Run retrospective analysis
retro_fit <- run_fims_retrospective(
  years_to_remove = 0:5,
  data = data1,
  parameters = parameters,
  n_cores = 1
)

# Calculate Mohn's rho for spawning biomass
rho_ssb <- calculate_mohns_rho(retro_fit, quantity = "spawning_biomass")

# Calculate Mohn's rho for recruitment
rho_rec <- calculate_mohns_rho(retro_fit, quantity = "expected_recruitment")
} # }