Incomplete Trip Estimation

Roving-Access Design Theory

The roving-access creel survey design combines two independent data streams (Pollock et al. 1994):

1. Instantaneous counts — total effort (angler-hours) via periodic counts
2. Complete trip interviews — catch per unit effort (CPUE) from anglers completing trips

This design is statistically optimal because:

• Counts provide unbiased effort estimates (snapshot of activity)
• Complete trip interviews provide unbiased CPUE (full trip information)
• Total catch = Effort × CPUE with independent variance estimation

Why Complete Trips Are Preferred

Complete trip interviews avoid length-of-stay bias. In roving-access designs, longer trips have higher probability of being sampled (they’re present for more count occasions). If incomplete trip catch rates differ systematically from complete trip catch rates—for example, if anglers who arrive early catch more fish per hour than late arrivals—then incomplete trip estimates will be biased.

Pollock et al. (1994) showed that:

• Complete trips provide unbiased CPUE estimates
• Incomplete trips suffer from length-of-stay bias unless catch rates are stationary
• Pooling complete and incomplete trips is invalid (different sampling probabilities)

For a roving-access survey, Pollock et al. (1994) recommend the following protocol:

• Default to complete trips only
• Require ≥10% of interviews to be complete trips
• Only use incomplete trips after validation
• Never auto-pool complete and incomplete trips

When Incomplete Trips Might Be Considered

Despite these concerns, incomplete-trip estimates can be valid when all of the following hold:

1. Stationary catch rates — catch per hour is similar throughout trip duration
2. Similar fishing behavior — complete and incomplete anglers fish the same way
3. Sufficient sample size — at least 30 incomplete trip interviews
4. Validation passes — TOST equivalence testing confirms similarity

Common scenarios for considering incomplete trips:

• Low complete trip sample size (but ≥10% threshold still met)
• Research questions specifically about incomplete trips
• Diagnostic comparisons to understand survey dynamics
• Exploring potential for future sampling protocols

Before considering incomplete trips, confirm that you have:

• Sufficient complete trip baseline (≥10% of interviews; Pollock et al. 1994)
• Adequate incomplete sample size (n ≥ 30 for stable estimates)
• Statistical validation using validate_incomplete_trips()
• Understanding of survey-specific fish behavior

Mean-of-Ratios vs. Ratio-of-Means

tidycreel uses different estimators for complete vs. incomplete trips:

Ratio-of-Means (complete trips, default):

CPUE = (Total Catch) / (Total Effort)

This estimator is appropriate for complete trips because it accounts for the correlation between catch and effort within each trip. Variance is computed using the delta method.

Mean-of-Ratios (incomplete trips):

CPUE = mean(Catch_i / Effort_i)

This estimator treats each incomplete trip’s catch rate as an independent observation. It’s used for incomplete trips because trip duration is unknown (trip not complete), making ratio-of-means inappropriate. The mean-of-ratios has higher variance but can be unbiased under stationarity assumptions.

For details on variance estimation, see ?estimate_catch_rate.

Default Workflow: Complete Trips Only

library(tidycreel)

# Standard workflow using complete trips (default)
data(example_calendar)
data(example_counts)
data(example_interviews)

design <- creel_design(example_calendar, date = date, strata = day_type) |>
  add_counts(example_counts) |>
  add_interviews(example_interviews,
    catch = catch_total,
    effort = hours_fished,
    harvest = catch_kept,
    trip_status = trip_status,
    trip_duration = trip_duration
  )

# Estimate CPUE using complete trips only (default)
cpue <- estimate_catch_rate(design)
print(cpue)

# Estimate total catch
total_catch <- estimate_total_catch(design)
print(total_catch)

The package defaults to complete trips and displays an informative message:

i Using complete trips for CPUE estimation
  (n=17, 77% of 22 interviews) [default]

Sample Size Requirements

Pollock et al. (1994) recommend that complete trips make up at least 10% of interviews. tidycreel checks this automatically:

# If complete trip percentage drops below 10%, you'll see:
# Warning: Only 8% of interviews (n=5) are complete trips
# Best practice: ≥10% of interviews should be complete trips
# Consider extending survey hours or sampling more trips to completion

This warning appears before sample-size validation, so it remains visible even when too few observations cause an error.

For details, see ?warn_low_complete_pct and Phase 18 documentation.

Pooling and substitution are different

Passing the TOST equivalence test does not permit pooling complete and incomplete trips. It supports a different decision:

• Pooling — combining raw complete and incomplete records into one dataset and estimating as if they are the same type. This is always invalid, because the differential sampling probabilities create bias that no equivalence test removes. TOST only tells you whether the resulting CPUE estimates happen to agree; it says nothing about the compatibility of the underlying sampling mechanisms.

• Substitution — choosing incomplete-trip estimates instead of complete-trip estimates as the sole basis for estimation. If TOST passes, use_trips = "incomplete" selects that trip type; it does not combine the two.

In short: validation passes → you may substitute; you may never pool.

What NOT to Do

# WRONG: Do not manually pool trip types
all_interviews <- rbind(complete_data, incomplete_data)
estimate_catch_rate(design_with_all_data) # INVALID — always, even after validation passes

# WRONG: Do not use custom weights to combine
weighted_mean(c(complete_cpue, incomplete_cpue)) # INVALID!

Package Design Prevents Auto-Pooling

tidycreel never auto-pools complete and incomplete trips:

• Unspecified (use_trips = NULL, the default): resolves to complete trips on an access-point design. On a roving design (interview_type = "roving") leaving it unspecified instead selects the all-trip mean-of-ratios estimator of Hoenig et al. (1997) — see “What the default does on a roving design” below. Naming either use_trips or estimator suppresses that routing.
• Explicit option: use_trips = "incomplete" for incomplete only (valid after passing validation)
• Diagnostic mode: use_trips = "diagnostic" for side-by-side comparison (not pooling)

There is no use_trips = "both" option because pooling is invalid.

“Pooling” here means one ratio-of-means fitted over complete and incomplete trips together, which is invalid because the two have different sampling probabilities. The roving route described above is not that: all-trip mean-of-ratios treats each contact’s catch rate as its own observation, which is what makes it valid over trips of unknown duration. It does use every contact, so if you need complete trips specifically, name them — the absence of a "both" option is not on its own a guarantee that you are getting complete-trip-only estimates.

What the default does on a roving design

Leaving use_trips unspecified is not the same as asking for complete trips.

On an access-point design the two are equivalent: an unspecified value resolves to complete trips. On a roving design they are not. When interview_type = "roving" and neither use_trips nor estimator is named, tidycreel selects the all-trip mean-of-ratios estimator of Hoenig et al. (1997), because that is the estimator the roving design calls for — not because complete trips were unavailable.

The method field reports which one ran, so the difference is visible rather than silent:

roving_design <- creel_design(
  example_calendar,
  date = date, strata = day_type,
  survey_type = "instantaneous", h_open = 14
) |>
  add_counts(example_counts, count_col = effort_hours) |>
  add_interviews(
    example_interviews,
    catch = catch_total, effort = hours_fished, n_anglers = n_anglers,
    harvest = catch_kept, trip_status = trip_status,
    trip_duration = trip_duration,
    interview_type = "roving"
  )
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
#> ℹ Added 22 interviews: 17 complete (77%), 5 incomplete (23%)

# Unspecified: routed to all-trip mean-of-ratios
estimate_catch_rate(roving_design)$method
#> ℹ Roving design: using all 22 interviews for CPUE via MOR [auto]
#>   (17 complete, 5 incomplete)
#>   Override with `use_trips = 'complete'` for access-point estimation.
#> ℹ MOR truncation: 0 trips excluded (all >= 0.5 hours)
#> Warning: Small sample size for CPUE estimation.
#> ! Sample size is 22. Ratio estimates are more stable with n >= 30.
#> ℹ Variance estimates may be unstable with n < 30.
#> [1] "mean-of-ratios-cpue"

# Named explicitly: complete trips, ratio-of-means
estimate_catch_rate(roving_design, use_trips = "complete")$method
#> ℹ Using complete trips for CPUE estimation
#>   (n=17, 77.3% of 22 interviews)
#> Warning: Small sample size for CPUE estimation.
#> ! Sample size is 17. Ratio estimates are more stable with n >= 30.
#> ℹ Variance estimates may be unstable with n < 30.
#> [1] "ratio-of-means-cpue"

The two answers differ, and on a roving design the routed one is usually the one you want. The point is that “the default” is not a synonym for “complete trips” on this design type. Wherever this vignette tells you to estimate from complete trips — including after a failed validation — name use_trips = "complete" rather than relying on the default to mean that.

If you need to compare complete vs. incomplete estimates, use diagnostic comparison mode (see section below) or validation workflow (next section).

Step 1: Load Data with Both Trip Types

library(tidycreel)

# Your survey data should have trip_status field
# Check trip type distribution
table(your_interviews$trip_status)

# Ensure you have:
# - At least 10% complete trips (Pollock et al. 1994)
# - At least 30 incomplete trips (for stable estimates)
# - At least 10 complete trips (for ratio estimation)

Step 2: Create Design and Attach Data

design <- creel_design(your_calendar, date = date, strata = day_type) |>
  add_counts(your_counts) |>
  add_interviews(your_interviews,
    catch = catch_total,
    effort = hours_fished,
    trip_status = trip_status,
    trip_duration = trip_duration
  )

Step 3: Run TOST Equivalence Testing

# Validate incomplete trips using TOST
validation <- validate_incomplete_trips(design,
  catch = catch_total,
  effort = hours_fished
)

print(validation)

The validate_incomplete_trips() function performs Two One-Sided Tests (TOST) to statistically test whether complete and incomplete trip CPUE estimates are equivalent within a threshold.

TOST explanation:

• Traditional t-test can only reject difference, not prove similarity
• TOST statistically proves estimates are “close enough”
• Tests null hypothesis: |difference| ≥ threshold
• Equivalence concluded when both one-sided tests reject (both p < 0.05)
• Standard approach for bioequivalence and ecological studies

Step 4: Interpret Results

If validation PASSES:

Incomplete Trip Validation (TOST Equivalence Test)

Overall Result: PASSED

Complete trips:   CPUE = 2.45 fish/hour (SE = 0.23, n = 45)
Incomplete trips: CPUE = 2.38 fish/hour (SE = 0.18, n = 120)

Equivalence threshold: ±20% of complete trip estimate (±0.49 fish/hour)
Difference: 0.07 fish/hour (3% of complete estimate)

TOST p-values: p1 = 0.012, p2 = 0.008
Equivalence: YES (both p < 0.05)

Recommendation: Incomplete trip estimates are statistically equivalent to
complete trip estimates within ±20% threshold. Safe to use incomplete trips
for this dataset.

If validation FAILS:

Incomplete Trip Validation (TOST Equivalence Test)

Overall Result: FAILED

Complete trips:   CPUE = 3.10 fish/hour (SE = 0.31, n = 38)
Incomplete trips: CPUE = 2.15 fish/hour (SE = 0.19, n = 95)

Equivalence threshold: ±20% of complete trip estimate (±0.62 fish/hour)
Difference: 0.95 fish/hour (31% of complete estimate)

TOST p-values: p1 = 0.234, p2 = 0.891
Equivalence: NO (at least one p >= 0.05)

Recommendation: Incomplete trip estimates are NOT equivalent to complete
trip estimates. Stick with complete trips only (Pollock et al. 1994).

Step 5: View Validation Plot

# Print method automatically shows plot
print(validation) # Plot appears after text output

# Or explicitly plot
plot(validation)

The validation plot shows a scatter plot with:

• Complete trip estimate on x-axis
• Incomplete trip estimate on y-axis
• Reference line at y = x (perfect agreement)
• Equivalence bounds as shaded region
• Color: blue if passed, red if failed

Step 6: Make Decision

If PASSED: - Safe to use use_trips = "incomplete" for this dataset - Consider using use_trips = "diagnostic" to compare estimates - Document validation results in your analysis notes - Revalidate if survey protocol or location changes

If FAILED: - Pass use_trips = "complete" explicitly — do not rely on the default (see “What the default does on a roving design”) - Do not use incomplete trip estimates - Investigate why estimates differ (time of day effects, early vs. late anglers) - Consider refining sampling protocol for future surveys

# Compare complete vs incomplete estimates
cpue_diagnostic <- estimate_catch_rate(design,
  catch = catch_total,
  effort = hours_fished,
  use_trips = "diagnostic"
)

print(cpue_diagnostic)

Diagnostic Comparison: Complete vs Incomplete Trip CPUE

trip_type    estimate    se  ci_lower  ci_upper   n
complete         2.45  0.23      2.00      2.90  45
incomplete       2.38  0.18      2.03      2.73 120

Difference: 0.07 fish/hour (3% of complete estimate)
Ratio: 1.03 (complete / incomplete)

Interpretation: Estimates differ by <10%, suggesting similar catch rates

When to Use Diagnostic Mode

Diagnostic mode is useful for:

• Exploring survey dynamics before formal validation
• Understanding differences between trip types
• Research questions about fishing patterns
• Teaching or demonstrating survey concepts
• Sensitivity analyses

Diagnostic mode is NOT a replacement for validation:

• Provides descriptive comparison, not statistical test
• No p-values or equivalence assessment
• No pass/fail recommendation
• Use validate_incomplete_trips() for decision-making

Interpretation Guidance

The diagnostic mode uses a 10% threshold for “substantial difference” (established in Phase 17):

• Difference < 10%: Estimates are similar, no practical difference
• Difference ≥ 10%: Estimates differ substantially, investigate further

This is a heuristic, not a statistical test. For formal validation, use validate_incomplete_trips().

TOST Equivalence Testing

Two One-Sided Tests (TOST) tests the null hypothesis:

H0: |μ_complete - μ_incomplete| ≥ δ
H1: |μ_complete - μ_incomplete| < δ

Where δ is the equivalence threshold (default ±20% of complete estimate).

Two one-sided tests:

1. Test 1: H0: μ_complete - μ_incomplete ≤ -δ vs H1: μ_complete - μ_incomplete > -δ
2. Test 2: H0: μ_complete - μ_incomplete ≥ δ vs H1: μ_complete - μ_incomplete < δ

Equivalence conclusion:

• Both p-values < 0.05 → equivalence confirmed (PASSED)
• At least one p ≥ 0.05 → equivalence not confirmed (FAILED)

For mathematical details and variance formulas, see ?validate_incomplete_trips.

Equivalence Threshold Configuration

The default equivalence threshold is ±20% of the complete trip estimate, appropriate for ecological field data. You can customize this:

# Use stricter threshold (±15%), keeping the previous setting to restore later
old_opts <- options(tidycreel.equivalence_threshold = 0.15)
validation_strict <- validate_incomplete_trips(design,
  catch = catch_total,
  effort = hours_fished
)

# Use more permissive threshold (±25%)
options(tidycreel.equivalence_threshold = 0.25)
validation_permissive <- validate_incomplete_trips(design,
  catch = catch_total,
  effort = hours_fished
)

# Restore the threshold that was in effect before
options(old_opts)

Choosing a threshold:

• Stricter (10-15%): High-stakes management decisions, research publications
• Default (20%): Standard ecological field studies, typical survey variability
• Permissive (25-30%): Exploratory analyses, preliminary surveys

The threshold should balance statistical rigor with realistic field variability. Consult with statistician or fisheries biologist for your specific application.

Trip Truncation

Incomplete trips with very short durations (<30 minutes) can inflate variance and bias estimates. tidycreel automatically truncates short incomplete trips using the Hoenig et al. (1997) recommended threshold:

# Default: truncate incomplete trips <0.5 hours (30 minutes)
cpue_incomplete <- estimate_catch_rate(design,
  use_trips = "incomplete",
  estimator = "mor",
  truncate_at = 0.5 # Default
)

# Custom truncation threshold
cpue_truncated <- estimate_catch_rate(design,
  use_trips = "incomplete",
  estimator = "mor",
  truncate_at = 1.0 # More conservative: only trips ≥1 hour
)

# Disable truncation (not recommended)
cpue_no_truncation <- estimate_catch_rate(design,
  use_trips = "incomplete",
  estimator = "mor",
  truncate_at = 0 # Includes all incomplete trips
)

The MOR print method shows truncation details:

Truncation: 8 of 120 incomplete trips removed (<0.5 hours)
Warning: 7% of incomplete trips truncated (>5% threshold)

For details on truncation methodology, see ?estimate_catch_rate and Phase 16 documentation.

Mean-of-Ratios Variance

The mean-of-ratios estimator computes:

CPUE_MOR = (1/n) * Σ(catch_i / effort_i)

Variance is estimated with the survey package, treating individual ratios as observations. The survey design is rebuilt after short incomplete trips are truncated so the variance calculation reflects the analytic sample.

This differs from ratio-of-means which uses delta method variance accounting for catch-effort covariance.

Decision Tree: Should I Use Incomplete Trips?

1. Do you have ≥10% complete trip interviews?
   • NO → Improve sampling protocol, extend survey hours
   • YES → Continue
2. Do you have ≥30 incomplete trip interviews?
   • NO → Sample size too small, stick with complete trips
   • YES → Continue
3. Have you run validate_incomplete_trips()?
   • NO → Run validation before proceeding
   • YES → Continue
4. Did validation PASS?
   • NO → Stick with complete trips only
   • YES → Safe to use incomplete trips for this dataset
5. Are you analyzing grouped estimates?
   • YES → Did ALL groups pass validation?
     • NO → Stick with complete trips
     • YES → Safe to use incomplete trips
   • NO → Proceed
6. Document validation results and proceed with incomplete trip estimation

Default Recommendations

For most creel surveys:

• Use complete trips only (default behavior)
• Follow the Pollock et al. (1994) protocol
• Aim for ≥10% complete trip interviews
• Sample size goal: n ≥ 30 complete trips per stratum

When considering incomplete trips:

• Validate using validate_incomplete_trips() FIRST
• Document validation results (passed/failed, p-values, threshold)
• Revalidate if survey protocol or location changes
• Monitor for seasonal or temporal changes in catch patterns

Never:

• Pool complete and incomplete trips without validation
• Use incomplete trips without statistical validation
• Auto-pool trip types (package prevents this by design)
• Trust incomplete estimates that failed validation

Function Reference

For detailed documentation, see:

• ?validate_incomplete_trips — TOST equivalence testing
• ?estimate_catch_rate — CPUE estimation with use_trips parameter
• ?add_interviews — Attach interview data with trip_status
• ?example_interviews — Example data with complete/incomplete trips

For complete trip estimation workflow, see the “Interview-Based Catch Estimation” vignette.

Further Reading

Key citations:

• Pollock, K.H., C.M. Jones, and T.L. Brown. 1994. Angler Survey Methods and Their Applications in Fisheries Management. American Fisheries Society Special Publication 25.
• Hoenig, J.M., C.M. Jones, K.H. Pollock, D.S. Robson, and D.L. Wade. 1997. Calculation of Catch Rate and Total Catch in Roving Surveys of Anglers. Biometrics 53:306-317.

Related package documentation:

• Phase 17: Complete Trip Defaults and Diagnostic Mode
• Phase 18: Sample Size Validation and Warnings
• Phase 19: TOST Equivalence Testing Framework
• Phase 16: Trip Truncation for Incomplete Interviews