GLMM-based aerial effort estimation with diurnal correction

Estimates total angler effort from aerial creel surveys using a generalized linear mixed model (GLMM), following the approach of Askey et al. (2018). When flights occur at non-random times of day, simple scaling of instantaneous counts can over- or under-estimate daily effort. This function fits a negative-binomial GLMM (or user-specified family) to model how angler counts change through the day, then integrates the fitted diurnal curve over the fishing day to obtain a bias-corrected effort estimate.

The default model is the quadratic temporal model from Askey (2018): count ~ poly(time_col, 2) + (1 | date), fitted via lme4::glmer.nb(). Variance is propagated via the delta method (default) or parametric bootstrap (lme4::bootMer()).

Usage

estimate_effort_aerial_glmm(
  design,
  time_col,
  formula = NULL,
  family = NULL,
  boot = FALSE,
  nboot = 500L,
  conf_level = 0.95
)

Arguments

design: A creel_design() object with design_type == "aerial" and counts attached via add_counts(). The counts data must contain the time-of-flight column specified by time_col.
time_col: Unquoted name of the numeric column in design$counts recording the hour of each aerial overflight (e.g., time_of_flight).
formula: Optional. A formula for the GLMM, passed directly to lme4::glmer.nb() or lme4::glmer(). If NULL (default), the Askey (2018) quadratic formula is used: count ~ poly(time_col, 2) + (1 | date).
family: Optional. A family object or character string specifying the GLM family. If NULL or "negbin" (default), lme4::glmer.nb() is used. Otherwise, lme4::glmer() is called with the specified family.
boot: Logical. If TRUE, use lme4::bootMer() for parametric bootstrap confidence intervals instead of the delta method. Default FALSE.
nboot: Integer. Number of bootstrap replicates when boot = TRUE. Default 500L.
conf_level: Numeric confidence level for the CI. Default 0.95.

Value

A creel_estimates object with:

estimate: total angler effort integrated over the fishing day
se: standard error (delta method or bootstrap SD)
se_between: same as se (fixed-effect SE component)
se_within: always NA_real_ — no Rasmussen within-day decomposition is performed for GLMM estimates
ci_lower, ci_upper: confidence interval bounds
n: number of count observations used to fit the model
method: "aerial_glmm_total"

Details

References

Askey, P.J., et al. (2018). Correcting for non-random flight timing in aerial creel surveys using a generalized linear mixed model. North American Journal of Fisheries Management, 38, 1204-1215. doi:10.1002/nafm.10010

Examples

if (FALSE) { # \dontrun{
data(example_aerial_glmm_counts)

aerial_cal <- unique(example_aerial_glmm_counts[, c("date", "day_type")])
aerial_cal <- aerial_cal[order(aerial_cal$date), ]
design <- creel_design(
  aerial_cal,
  date = date,
  strata = day_type,
  survey_type = "aerial",
  h_open = 14
)
design <- add_counts(design, example_aerial_glmm_counts)

# Default Askey quadratic model with delta-method SE
result <- estimate_effort_aerial_glmm(design, time_col = time_of_flight)
print(result)

# Bootstrap CIs (slower)
result_boot <- estimate_effort_aerial_glmm(
  design,
  time_col = time_of_flight,
  boot = TRUE,
  nboot = 100L
)
print(result_boot)
} # }