Estimate design-weighted mean length from a creel length distribution

est_mean_length() computes the pressure-weighted mean fish length from a est_length_distribution() object using the ratio estimator \(\bar{L} = \sum_h L_h \hat{N}_h / \sum_h \hat{N}_h\), with delta-method standard error.

Usage

est_mean_length(ld, conf_level = NULL)

Arguments

ld

A creel_length_distribution object from est_length_distribution().

conf_level

Numeric confidence level for confidence intervals. Defaults to the level stored in ld (usually 0.95).

Value

A data.frame with class c("creel_mean_length", "data.frame") and columns: grouping columns (if any), mean_length, mean_length_se, mean_length_ci_lower, mean_length_ci_upper. Rows where the total estimated fish is zero or negative return NA for all numeric columns with a warning.

Details

Bin midpoints \(L_h = (\text{bin\_lower} + \text{bin\_upper}) / 2\) serve as representative lengths. Mean length is the ratio of total length-weighted count to total count: $$\bar{L} = \frac{\sum_h L_h \hat{N}_h}{\hat{N}}$$

Variance is propagated via the delta method for a ratio estimator, using the bins' full covariance matrix \(\Sigma\): $$\widehat{\text{Var}}(\bar{L}) = \frac{1}{\hat{N}^2} w' \Sigma w, \quad w_h = L_h - \bar{L}$$ Earlier versions treated the cross-bin covariances as zero, which under-estimated the standard error. If \(\Sigma\) is unavailable the independence form is used and a warning says so.

See also

Other "Estimation": compare_cpue_estimators(), est_age_distribution(), est_biomass(), est_compliance(), est_effort_camera_mi(), est_length_distribution(), est_mean_age(), estimate_catch_rate(), estimate_effort(), estimate_effort_aerial_glmm(), estimate_harvest_rate(), estimate_release_rate(), estimate_total_catch(), estimate_total_harvest(), estimate_total_release()

Examples

data(example_calendar)
data(example_interviews)
data(example_lengths)
data(example_catch)


design <- creel_design(example_calendar, date = date, strata = day_type)
design <- add_interviews(design, example_interviews,
  catch = catch_total, effort = hours_fished, harvest = catch_kept,
  trip_status = trip_status
)
#> Warning: ! No `n_anglers` provided — assuming 1 angler per interview.
#> ℹ Pass `n_anglers = <column>` to use actual party sizes for angler-hour
#>   normalization.
#> ℹ If the interviews really are one angler each, pass `n_anglers = 1` to state
#>   that and silence this warning.
#> ℹ Added 22 interviews: 17 complete (77%), 5 incomplete (23%)
# Species catch is required to group by species: the totals are scaled onto
# the reported catch, and only this table records it per species.
design <- add_catch(design, example_catch,
  catch_uid = interview_id,
  interview_uid = interview_id,
  species = species,
  count = count,
  catch_type = catch_type
)
design <- add_lengths(design, example_lengths,
  length_uid = interview_id,
  interview_uid = interview_id,
  species = species,
  length = length,
  length_type = length_type,
  count = count,
  release_format = "binned"
)

ld <- est_length_distribution(design, by = species, bin_width = 25)
#> Warning: ! Length totals were rescaled onto the reported catch.
#> ℹ Measured fish (weighted): 37; reported: 93 -- a factor of 2.51.
#> ℹ estimate, se and the confidence bounds describe the REPORTED catch, estimated
#>   from the measured subsample. Shares (percent) are unaffected.
est_mean_length(ld)
#>   species mean_length mean_length_se mean_length_ci_lower mean_length_ci_upper
#> 1    bass    300.9615       11.97037             277.5000             324.4230
#> 2 panfish    196.5909        9.12372             178.7087             214.4731
#> 3 walleye    431.7308       14.13632             404.0241             459.4374