Temporal Extrapolation

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Overview

Creel surveys sample a fraction of days in a season. Design-based estimators in tidycreel automatically account for unsampled days through survey weights — so when you call estimate_effort() or estimate_total_catch(), the result is already a season-total estimate, not just a sample-day sum.

The examples show how to:

Obtain a full-season total from a single design
Break the season into monthly totals using separate monthly designs
Combine monthly estimates to a season or annual total
Assemble multi-estimate reports with season_summary()

How Design-Based Extrapolation Works

When you create a design with creel_design(), the survey object assigns a weight to each sampled day. A day sampled at rate $f$ receives weight $1/f$, so its observed angler-hours represent $1/f$ days of that stratum type. The estimator then sums weighted observations across strata to produce a population total for the entire design period.

In practice this means:

A season design covering May–September gives you a season-total estimate.
A monthly design covering just June gives you a June-total estimate.
You do not need to multiply results by any “expansion factor” — the weights already perform the extrapolation.

The same target logic applies when the calendar includes schedule-defined special strata. If generate_schedule(..., special_periods = ...) resolved opener or holiday days into a final analysis stratum, estimate_effort(..., target = "stratum_total") and target = "period_total" expand within those declared strata exactly as they do for the usual weekday/weekend case. The important constraint is that the calendar passed to creel_design() must use the resolved final analysis stratum rather than the old baseline label. Sparse special strata still trigger the usual variance diagnostics: warnings for unstable small strata and explicit single-PSU errors when variance cannot be estimated.

Building a Season-Long Dataset

library(tidycreel)

set.seed(2024)

# Full season: May 1 – September 30 (184 days)
all_dates <- seq(as.Date("2024-05-01"), as.Date("2024-09-30"), by = "1 day")
day_types <- ifelse(
  as.integer(format(all_dates, "%u")) %in% c(6L, 7L), "weekend", "weekday"
)

season_calendar <- data.frame(
  date     = all_dates,
  day_type = day_types
)

# Stratified random sample: 30% of weekdays, 50% of weekends
set.seed(2024)
sampled <- ave(
  seq_along(all_dates), day_types,
  FUN = function(i) {
    rate <- if (day_types[i[1]] == "weekend") 0.50 else 0.30
    as.integer(runif(length(i)) < rate)
  }
)
sampled_calendar <- season_calendar[as.logical(sampled), ]

# Generate plausible effort counts (angler-hours per count)
# Weekend counts higher than weekday
sampled_counts <- data.frame(
  date = sampled_calendar$date,
  day_type = sampled_calendar$day_type,
  n_anglers = ifelse(
    sampled_calendar$day_type == "weekend",
    round(rnorm(sum(sampled), mean = 55, sd = 18)),
    round(rnorm(sum(sampled), mean = 28, sd = 12))
  )
)
sampled_counts$n_anglers <- pmax(sampled_counts$n_anglers, 0L)

nrow(sampled_calendar) # Number of sampled days
#> [1] 58

Season-Total Effort

Pass the sampled calendar to creel_design(), attach the counts, and call estimate_effort(). The result is the estimated total angler-hours for the entire May–September season.

season_design <- creel_design(
  sampled_calendar,
  date = date, strata = day_type
)
season_design <- add_counts(season_design, sampled_counts)
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability

season_effort <- estimate_effort(season_design)
season_effort$estimates
#> # A tibble: 1 × 7
#>   estimate    se se_between se_within ci_lower ci_upper     n
#>      <dbl> <dbl>      <dbl>     <dbl>    <dbl>    <dbl> <int>
#> 1     2004  121.       121.         0    1763.    2245.    58

The estimate column is the season-total angler-hours; se is the standard error of that total.

Monthly Effort Totals

To break the season into monthly totals, subset the calendar and counts to each month, build a separate monthly design, and estimate. Monthly designs are independent, so their variances can be combined later.

months <- 5:9
month_labels <- c("May", "June", "July", "August", "September")

monthly_effort <- lapply(seq_along(months), function(i) {
  m <- months[i]
  cal_m <- sampled_calendar[format(sampled_calendar$date, "%m") == sprintf("%02d", m), ]
  cnt_m <- sampled_counts[format(sampled_counts$date, "%m") == sprintf("%02d", m), ]

  if (nrow(cal_m) == 0) {
    return(NULL)
  }

  des_m <- creel_design(cal_m, date = date, strata = day_type)
  des_m <- add_counts(des_m, cnt_m)
  est <- estimate_effort(des_m)$estimates

  cbind(month = month_labels[i], est)
})
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability

do.call(rbind, monthly_effort)
#>       month estimate       se se_between se_within ci_lower ci_upper  n
#> 1       May      257 45.19735   45.19735         0 150.1253 363.8747  9
#> 2      June      461 73.10814   73.10814         0 300.0901 621.9099 13
#> 3      July      338 57.00058   57.00058         0 206.5564 469.4436 10
#> 4    August      491 55.13036   55.13036         0 369.6589 612.3411 13
#> 5 September      457 39.73244   39.73244         0 369.5495 544.4505 13

Season Total from Monthly Estimates

Because monthly estimates are independent (non-overlapping time windows), the season total is the sum of monthly estimates and the season variance is the sum of monthly variances.

monthly_df <- do.call(rbind, monthly_effort)

season_from_months <- data.frame(
  stratum  = "Season total",
  estimate = sum(monthly_df$estimate),
  se       = sqrt(sum(monthly_df$se^2))
)

season_from_months
#>        stratum estimate       se
#> 1 Season total     2004 123.5099

This should be close to the single-design season total above (small differences are due to independent stratification within each monthly design).

Monthly Catch Totals

Total catch estimation follows the same monthly pattern: estimate the catch rate from interviews, then multiply by monthly effort. First, generate synthetic interview data:

set.seed(2024)

# Three interviews per sampled day (ensures ≥10 complete trips per month)
n_per_day <- 3L
n_int <- nrow(sampled_calendar) * n_per_day
catch_total <- rpois(n_int, lambda = 1.8)
interviews <- data.frame(
  date         = rep(sampled_calendar$date, each = n_per_day),
  day_type     = rep(sampled_calendar$day_type, each = n_per_day),
  trip_status  = "complete",
  hours_fished = round(rnorm(n_int, mean = 3.5, sd = 1.2), 1),
  catch_total  = catch_total,
  catch_kept   = pmin(rpois(n_int, lambda = 0.6), catch_total)
)
interviews$hours_fished <- pmax(interviews$hours_fished, 0.5)

Then loop over months exactly as for effort:

monthly_catch <- lapply(seq_along(months), function(i) {
  m <- months[i]
  cal_m <- sampled_calendar[format(sampled_calendar$date, "%m") == sprintf("%02d", m), ]
  cnt_m <- sampled_counts[format(sampled_counts$date, "%m") == sprintf("%02d", m), ]
  int_m <- interviews[format(interviews$date, "%m") == sprintf("%02d", m), ]

  if (nrow(cal_m) == 0) {
    return(NULL)
  }

  des_m <- creel_design(cal_m, date = date, strata = day_type)
  des_m <- add_counts(des_m, cnt_m)
  des_m <- add_interviews(des_m, int_m,
    trip_status = trip_status,
    catch = catch_total,
    effort = hours_fished,
    n_anglers = 1, # every interview is a single angler
    harvest = catch_kept
  )

  effort_est <- estimate_effort(des_m)
  catch_est <- estimate_total_catch(des_m)

  cbind(month = month_labels[i], catch_est$estimates)
})
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
#> Warning: 5 interviews have zero catch.
#> ℹ Zero catch may be valid (skunked) or indicate missing data.
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
#> Warning: 7 interviews have zero catch.
#> ℹ Zero catch may be valid (skunked) or indicate missing data.
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
#> Warning: 4 interviews have zero catch.
#> ℹ Zero catch may be valid (skunked) or indicate missing data.
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
#> Warning: 9 interviews have zero catch.
#> ℹ Zero catch may be valid (skunked) or indicate missing data.
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
#> Warning: 7 interviews have zero catch.
#> ℹ Zero catch may be valid (skunked) or indicate missing data.

do.call(rbind, monthly_catch)
#>       month estimate       se  ci_lower ci_upper  n
#> 1       May 135.4235 32.19588  69.11487 201.7322 27
#> 2      June 209.1243 43.65869 120.66337 297.5852 39
#> 3      July 143.0169 32.42928  76.58848 209.4452 30
#> 4    August 236.6189 41.48349 152.56536 320.6724 39
#> 5 September 217.9545 38.61587 139.71136 296.1977 39

Season-Total Catch

Sum the monthly totals:

catch_df <- do.call(rbind, monthly_catch)
season_catch <- data.frame(
  stratum  = "Season total",
  estimate = sum(catch_df$estimate),
  se       = sqrt(sum(catch_df$se^2))
)
season_catch
#>        stratum estimate      se
#> 1 Season total 942.1381 84.8904

Assembling a Summary Report

season_summary() assembles multiple creel_estimates objects into a single wide tibble for reporting. For a monthly summary, build a list with named entries and pass it to season_summary().

# Collect effort and catch estimates for each month into named lists
effort_list <- list()
catch_list <- list()

for (i in seq_along(months)) {
  m <- months[i]
  label <- month_labels[i]

  cal_m <- sampled_calendar[format(sampled_calendar$date, "%m") == sprintf("%02d", m), ]
  cnt_m <- sampled_counts[format(sampled_counts$date, "%m") == sprintf("%02d", m), ]
  int_m <- interviews[format(interviews$date, "%m") == sprintf("%02d", m), ]

  if (nrow(cal_m) == 0) next

  des_m <- creel_design(cal_m, date = date, strata = day_type)
  des_m <- add_counts(des_m, cnt_m)
  des_m <- add_interviews(des_m, int_m,
    trip_status = trip_status,
    catch = catch_total,
    effort = hours_fished,
    n_anglers = 1, # every interview is a single angler
    harvest = catch_kept
  )

  effort_list[[label]] <- estimate_effort(des_m)
  catch_list[[label]] <- estimate_total_catch(des_m)
}
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
#> Warning: 5 interviews have zero catch.
#> ℹ Zero catch may be valid (skunked) or indicate missing data.
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
#> Warning: 7 interviews have zero catch.
#> ℹ Zero catch may be valid (skunked) or indicate missing data.
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
#> Warning: 4 interviews have zero catch.
#> ℹ Zero catch may be valid (skunked) or indicate missing data.
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
#> Warning: 9 interviews have zero catch.
#> ℹ Zero catch may be valid (skunked) or indicate missing data.
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
#> Warning: 7 interviews have zero catch.
#> ℹ Zero catch may be valid (skunked) or indicate missing data.

# Assemble effort report
effort_summary <- season_summary(effort_list)
effort_summary$table
#> # A tibble: 1 × 35
#>   May_estimate May_se May_se_between May_se_within May_ci_lower May_ci_upper
#>          <dbl>  <dbl>          <dbl>         <dbl>        <dbl>        <dbl>
#> 1          257   45.2           45.2             0         150.         364.
#> # ℹ 29 more variables: May_n <int>, June_estimate <dbl>, June_se <dbl>,
#> #   June_se_between <dbl>, June_se_within <dbl>, June_ci_lower <dbl>,
#> #   June_ci_upper <dbl>, June_n <int>, July_estimate <dbl>, July_se <dbl>,
#> #   July_se_between <dbl>, July_se_within <dbl>, July_ci_lower <dbl>,
#> #   July_ci_upper <dbl>, July_n <int>, August_estimate <dbl>, August_se <dbl>,
#> #   August_se_between <dbl>, August_se_within <dbl>, August_ci_lower <dbl>,
#> #   August_ci_upper <dbl>, August_n <int>, September_estimate <dbl>, …

catch_summary <- season_summary(catch_list)
catch_summary$table
#> # A tibble: 1 × 25
#>   May_estimate May_se May_ci_lower May_ci_upper May_n June_estimate June_se
#>          <dbl>  <dbl>        <dbl>        <dbl> <int>         <dbl>   <dbl>
#> 1         135.   32.2         69.1         202.    27          209.    43.7
#> # ℹ 18 more variables: June_ci_lower <dbl>, June_ci_upper <dbl>, June_n <int>,
#> #   July_estimate <dbl>, July_se <dbl>, July_ci_lower <dbl>,
#> #   July_ci_upper <dbl>, July_n <int>, August_estimate <dbl>, August_se <dbl>,
#> #   August_ci_lower <dbl>, August_ci_upper <dbl>, August_n <int>,
#> #   September_estimate <dbl>, September_se <dbl>, September_ci_lower <dbl>,
#> #   September_ci_upper <dbl>, September_n <int>

Annual Totals Across Multiple Seasons

When survey data span multiple calendar years, apply the same pattern at the year level: build one design per year, run estimators, then sum totals and combine variances.

# Conceptual pattern — replace with actual data per year
year_effort <- list()

for (yr in c(2022, 2023, 2024)) {
  cal_yr <- subset(full_calendar, format(date, "%Y") == yr)
  cnt_yr <- subset(full_counts, format(date, "%Y") == yr)

  des_yr <- creel_design(cal_yr, date = date, strata = day_type)
  des_yr <- add_counts(des_yr, cnt_yr)

  year_effort[[as.character(yr)]] <- estimate_effort(des_yr)
}

# Multi-year report table
season_summary(year_effort)$table

Exporting Results

write_schedule() accepts any data frame, so you can export the assembled summary table directly:

write_schedule(effort_summary$table, "effort_by_month_2024.csv")
write_schedule(effort_summary$table, "effort_by_month_2024.xlsx")

Practical reminders

Goal	Approach
Season total	Single design covering full season; call `estimate_effort()` once
Monthly totals	Separate monthly designs; loop over months
Season total from months	Sum monthly estimates; sum monthly variances
Annual comparison	Separate annual designs; use `season_summary()`
Report table	`season_summary(named_list_of_estimates)$table`

References

Cochran, W. G. (1977). Sampling Techniques, 3rd ed. Wiley, New York.
Pollock, K. H., Jones, C. M., and Brown, T. L. (1994). Angler Survey Methods and Their Applications in Fisheries Management. American Fisheries Society, Bethesda, MD.
Su, Y.-S., and Liu, P. (2025). Flexible creel survey estimators. Canadian Journal of Fisheries and Aquatic Sciences, 82, 1–27.

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