Variance Methods: Taylor, Bootstrap, and Jackknife

tidycreel exposes three variance estimation methods through the variance argument of estimate_effort(), estimate_catch_rate(), and related functions:

variance =	Description	Requires
"taylor"	Taylor linearization (default)	≥ 2 PSUs per stratum recommended
"bootstrap"	Bootstrap resampling (500 replicates)	≥ 2 PSUs per stratum
"jackknife"	Delete-one jackknife	≥ 2 PSUs per stratum

library(tidycreel)

---

1 Building a design for the examples

All three methods work on the same creel_design object. Here we use the bundled example_counts and example_interviews datasets, which have 10 sampled weekdays and 4 sampled weekends.

data("example_counts")
data("example_interviews")

cal <- unique(example_counts[, c("date", "day_type")])
design <- creel_design(cal, date = date, strata = day_type)
design <- add_counts(design, example_counts)
design <- add_interviews(
  design, example_interviews,
  catch = catch_total,
  effort = hours_fished,
  trip_status = trip_status
)
#> ℹ No `n_anglers` provided — assuming 1 angler per interview.
#> ℹ Pass `n_anglers = <column>` to use actual party sizes for angler-hour
#>   normalization.
#> ℹ Added 22 interviews: 17 complete (77%), 5 incomplete (23%)

---

2 Comparing the three variance methods

Pass variance = "..." to any estimator. The point estimate is identical across methods; only the SE and CI change.

eff_taylor <- estimate_effort(design, variance = "taylor")
eff_bootstrap <- estimate_effort(design, variance = "bootstrap")
eff_jackknife <- estimate_effort(design, variance = "jackknife")

# Summarise all three for comparison
rbind(
  as.data.frame(summary(eff_taylor)),
  as.data.frame(summary(eff_bootstrap)),
  as.data.frame(summary(eff_jackknife))
)
#>   Estimate    SE CI Lower CI Upper  N
#> 1    372.5 13.18    343.8    401.2 14
#> 2    372.5 13.20    343.7    401.3 14
#> 3    372.5 13.18    343.8    401.2 14

With 10–14 PSUs per stratum the three methods produce very similar standard errors. This convergence is expected: bootstrap and jackknife are asymptotically equivalent to Taylor linearization for simple probability samples.

---

3 When to use each method

Taylor linearization ("taylor", default)

• Use when: stratum-level variance is dominated by between-day variability and the sampling design is a straightforward stratified random sample of days.
• Advantage: fastest; closed-form analytic variance formula; no randomness.
• Limitation: relies on large-sample approximations; can be less reliable for highly skewed count distributions or very small strata.

Bootstrap ("bootstrap")

• Use when: count distributions are highly skewed, the design is complex, or you want variance that is robust to distributional assumptions.
• Advantage: makes no distributional assumption; captures nonlinear variance propagation.
• Limitation: stochastic (set a seed in your script for reproducibility); slower (500 replicates by default); requires ≥ 2 PSUs per stratum.

Jackknife ("jackknife")

• Use when: you prefer a deterministic, delete-one variance estimate that is slightly more conservative than Taylor for small samples.
• Advantage: deterministic; often more stable than bootstrap with small PSU counts.
• Limitation: also requires ≥ 2 PSUs per stratum; not appropriate for designs with unequal inclusion probabilities unless the correct jackknife weights are applied.

---

4 Grouped estimates

All three methods work with the by argument.

eff_grp_taylor <- estimate_effort(design, by = day_type, variance = "taylor")
eff_grp_bootstrap <- estimate_effort(design, by = day_type, variance = "bootstrap")

rbind(
  cbind(method = "taylor", as.data.frame(summary(eff_grp_taylor))),
  cbind(method = "bootstrap", as.data.frame(summary(eff_grp_bootstrap)))
)
#>      method day_type Estimate     SE CI Lower CI Upper  N
#> 1    taylor  weekday    170.6  9.674    149.5    191.7 10
#> 2    taylor  weekend    201.9  8.946    182.4    221.4  4
#> 3 bootstrap  weekday    170.6 10.230    148.3    192.9 10
#> 4 bootstrap  weekend    201.9  8.604    183.2    220.6  4

---

5 Single-PSU diagnostic

All three variance methods require at least 2 PSUs (sampled days) per stratum. When a stratum has only 1 sampled day, tidycreel raises a structured error naming the stratum:

# Build a minimal design with 1 sampled day per stratum
dates_1psu <- c(as.Date("2024-06-03"), as.Date("2024-06-08"))
cal_1psu <- data.frame(date = dates_1psu, day_type = c("weekday", "weekend"))
d_1psu <- creel_design(cal_1psu, date = date, strata = day_type)
counts_1psu <- data.frame(
  date     = dates_1psu,
  day_type = c("weekday", "weekend"),
  count    = c(10L, 15L)
)
d_1psu <- add_counts(d_1psu, counts_1psu)

# Taylor linearization raises an error when variance cannot be estimated
estimate_effort(d_1psu, variance = "jackknife")
#> Error in `value[[3L]]()`:
#> ! Stratum "weekday" has only 1 PSU — jackknife variance cannot be
#>   estimated.
#> ✖ A stratum must have at least 2 PSUs for jackknife resampling.
#> ℹ Increase the sampling rate for stratum "weekday", or use `variance =
#>   'taylor'`.

The error message names the problematic stratum ("weekday") and suggests either increasing the sampling rate or switching to variance = "taylor" which can still produce a point estimate via the lonely-PSU adjustment.

---

6 Summary

Variance method comparison

Method	Deterministic	Min PSUs	Speed	When to prefer
taylor	Yes	1 (with lonely-PSU adjust)	Fast	Default; simple designs
bootstrap	No (stochastic)	2	Slow (500 replicates)	Skewed counts; complex designs
jackknife	Yes	2	Moderate	Small samples; deterministic alternative to bootstrap