---
title: "Incomplete Trip Estimation"
output:
  rmarkdown::html_vignette:
    highlight: null
vignette: >
  %\VignetteIndexEntry{Incomplete Trip Estimation}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
library(tidycreel)
```

## Introduction

This vignette explains when and how incomplete-trip interviews can support catch estimation in roving-access creel surveys. The usual design uses complete-trip interviews, following Pollock et al. (1994). Incomplete-trip estimates may be appropriate in limited circumstances, but only after validation.

Use complete trips by default. Before relying on incomplete trips, run the required statistical validation with `validate_incomplete_trips()`. Never pool complete and incomplete trips: their sampling probabilities differ.

This vignette shows:

1. Scientific rationale for complete trip preference
2. The recommended field protocol
3. When incomplete trip estimation might be considered
4. Step-by-step validation workflow
5. Realistic examples of passing and failing validation
6. Diagnostic comparison mode for research purposes

## Scientific Rationale

### 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`.

## Recommended field protocol

The following roving-access standards follow Pollock et al. (1994).

### Default Workflow: Complete Trips Only

```{r complete_example, eval=FALSE}
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:

```{r low_complete_warning, eval=FALSE}
# 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.

## Never pool complete and incomplete trips

Pooling complete and incomplete trips is scientifically invalid, even when validation passes.

Complete and incomplete trips have **different sampling probabilities** in roving-access designs. Longer trips have higher probability of being sampled during their incomplete phase, creating systematic bias if pooled with complete trips.

### 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

```{r anti_pattern, eval=FALSE}
# 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:

```{r roving-default}
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"
  )

# Unspecified: routed to all-trip mean-of-ratios
estimate_catch_rate(roving_design)$method

# Named explicitly: complete trips, ratio-of-means
estimate_catch_rate(roving_design, use_trips = "complete")$method
```

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-by-Step Validation Workflow

Before using incomplete-trip estimates, validate that they agree sufficiently with complete-trip estimates. The workflow is:

### Step 1: Load Data with Both Trip Types

```{r validation_setup, eval=FALSE}
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

```{r validation_design, eval=FALSE}
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

```{r run_validation, eval=FALSE}
# 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

```{r validation_plot, eval=FALSE}
# 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

## Example: Validation Passes

Here's a realistic scenario where incomplete trip validation passes because catch rates are stationary throughout the day.

```{r example_pass}
library(tidycreel)

# Simulate data where catch rates are similar for complete vs incomplete
set.seed(42)

# Create calendar
calendar <- data.frame(
  date = seq.Date(as.Date("2024-06-01"), as.Date("2024-06-14"), by = "day"),
  day_type = rep(c("weekday", "weekend"), length.out = 14)
)

# Create counts
counts <- data.frame(
  date = calendar$date,
  day_type = calendar$day_type,
  effort_hours = round(runif(14, min = 50, max = 150))
)

# Simulate interviews with SIMILAR catch rates for both trip types
# (stationary catch rate throughout day)
n_complete <- 50
n_incomplete <- 120

# Base CPUE around 2.4 fish/hour for both groups (PASSING scenario)
complete_interviews <- data.frame(
  date = sample(calendar$date, n_complete, replace = TRUE),
  hours_fished = runif(n_complete, min = 2, max = 8),
  trip_status = "complete",
  trip_duration = runif(n_complete, min = 2, max = 8)
)
complete_interviews$catch_total <- rpois(n_complete,
  lambda = complete_interviews$hours_fished * 2.4
)

incomplete_interviews <- data.frame(
  date = sample(calendar$date, n_incomplete, replace = TRUE),
  hours_fished = runif(n_incomplete, min = 1, max = 6),
  trip_status = "incomplete"
)
# For incomplete trips, trip_duration = hours_fished (time interviewed, not total trip)
incomplete_interviews$trip_duration <- incomplete_interviews$hours_fished
# Similar CPUE for incomplete trips (2.3-2.5 range)
incomplete_interviews$catch_total <- rpois(n_incomplete,
  lambda = incomplete_interviews$hours_fished * 2.35
)

interviews <- rbind(complete_interviews, incomplete_interviews)

# Create design
design <- creel_design(calendar, date = date, strata = day_type) |>
  add_counts(counts) |>
  add_interviews(interviews,
    catch = catch_total,
    effort = hours_fished,
    trip_status = trip_status,
    trip_duration = trip_duration
  )

# Run validation
validation_pass <- validate_incomplete_trips(design,
  catch = catch_total,
  effort = hours_fished
)

print(validation_pass)
```

**Interpretation:**

- Complete and incomplete CPUE estimates are very close (within ~5%)
- Both TOST p-values < 0.05 → equivalence confirmed
- Validation PASSED → safe to use incomplete trips for this dataset
- Plot shows estimates within equivalence bounds

**Next steps after passing validation:**

```{r after_pass, eval=FALSE}
# Now safe to use incomplete trips
cpue_incomplete <- estimate_catch_rate(design, use_trips = "incomplete")
print(cpue_incomplete)

# Or use diagnostic mode to compare
cpue_diagnostic <- estimate_catch_rate(design, use_trips = "diagnostic")
print(cpue_diagnostic)
```

## Example: Validation Fails

Here's a realistic scenario where validation fails because early-morning anglers catch fish at higher rates than afternoon anglers.

```{r example_fail}
library(tidycreel)
set.seed(123)

# Same calendar and counts as before
calendar <- data.frame(
  date = seq.Date(as.Date("2024-06-01"), as.Date("2024-06-14"), by = "day"),
  day_type = rep(c("weekday", "weekend"), length.out = 14)
)

counts <- data.frame(
  date = calendar$date,
  day_type = calendar$day_type,
  effort_hours = round(runif(14, min = 50, max = 150))
)

# Simulate interviews with DIFFERENT catch rates (FAILING scenario)
# Complete trips average full day (includes productive morning hours)
# Incomplete trips are mostly afternoon interviews (lower catch rates)

n_complete <- 45
n_incomplete <- 110

# Complete trips: higher CPUE (includes morning fishing, ~3.0 fish/hour)
complete_interviews <- data.frame(
  date = sample(calendar$date, n_complete, replace = TRUE),
  hours_fished = runif(n_complete, min = 3, max = 8),
  trip_status = "complete",
  trip_duration = runif(n_complete, min = 3, max = 8)
)
complete_interviews$catch_total <- rpois(n_complete,
  lambda = complete_interviews$hours_fished * 3.0
)

# Incomplete trips: lower CPUE (afternoon interviews, ~2.0 fish/hour)
incomplete_interviews <- data.frame(
  date = sample(calendar$date, n_incomplete, replace = TRUE),
  hours_fished = runif(n_incomplete, min = 1, max = 5),
  trip_status = "incomplete"
)
# For incomplete trips, trip_duration = hours_fished (time interviewed, not total trip)
incomplete_interviews$trip_duration <- incomplete_interviews$hours_fished
incomplete_interviews$catch_total <- rpois(n_incomplete,
  lambda = incomplete_interviews$hours_fished * 2.0
)

interviews_biased <- rbind(complete_interviews, incomplete_interviews)

# Create design
design_biased <- creel_design(calendar, date = date, strata = day_type) |>
  add_counts(counts) |>
  add_interviews(interviews_biased,
    catch = catch_total,
    effort = hours_fished,
    trip_status = trip_status,
    trip_duration = trip_duration
  )

# Run validation
validation_fail <- validate_incomplete_trips(design_biased,
  catch = catch_total,
  effort = hours_fished
)

print(validation_fail)
```

**Interpretation:**

- Complete trip CPUE (~3.0) is substantially higher than incomplete CPUE (~2.0)
- Difference is ~33% of complete estimate, exceeds ±20% threshold
- At least one TOST p-value ≥ 0.05 → equivalence NOT confirmed
- Validation FAILED → stick with complete trips only
- Plot shows estimates outside equivalence bounds (red)

**Correct action after failing validation:**

```{r after_fail, eval=FALSE}
# DO NOT use incomplete trips
# Stick with default complete trip estimation
# `design_biased` is an access-point design, so an unspecified `use_trips`
# resolves to complete trips. On a roving design it would not -- name it.
cpue_complete <- estimate_catch_rate(design_biased, use_trips = "complete")
print(cpue_complete)

# Investigate why estimates differ
# Possible reasons:
# - Time-of-day effects (morning vs afternoon catch rates)
# - Trip length correlates with skill level
# - Fish behavior changes throughout day (feeding windows)
# - Different angler types (early vs late arrivals)
```

## Using Diagnostic Comparison Mode

For research purposes or to understand your survey dynamics, use **diagnostic comparison mode** to see complete and incomplete estimates side-by-side without statistical testing.

```{r diagnostic_mode, eval=FALSE}
# Compare complete vs incomplete estimates
cpue_diagnostic <- estimate_catch_rate(design,
  catch = catch_total,
  effort = hours_fished,
  use_trips = "diagnostic"
)

print(cpue_diagnostic)
```

**Example output:**

```
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()`.

## Advanced: Grouped Validation

When estimating CPUE by strata (e.g., by day type), validate within each group:

```{r grouped_validation, eval=FALSE}
# Validate with grouping
validation_grouped <- validate_incomplete_trips(design,
  catch = catch_total,
  effort = hours_fished,
  by = day_type
)

print(validation_grouped)
```

**Grouped validation requires:**

- Overall equivalence (all groups combined)
- **AND** per-group equivalence (each group separately)

This conservative approach prevents overlooking group-specific bias that could be masked by overall equivalence.

**Example grouped output:**

```
Incomplete Trip Validation (Grouped by day_type)

Overall Result: FAILED

Overall (ungrouped):
  Complete: 2.45 fish/hour (n=45)
  Incomplete: 2.38 fish/hour (n=120)
  TOST: PASSED (p1=0.012, p2=0.008)

Group: weekday
  Complete: 2.20 fish/hour (n=20)
  Incomplete: 2.15 fish/hour (n=55)
  TOST: PASSED (p1=0.031, p2=0.019)

Group: weekend
  Complete: 2.80 fish/hour (n=25)
  Incomplete: 2.45 fish/hour (n=65)
  TOST: FAILED (p1=0.156, p2=0.234)

Recommendation: Overall equivalence passed but weekend group failed.
Do not use incomplete trips. Investigate group-specific differences.
```

Even though overall validation passed, the weekend group failed—incomplete trip estimates are biased on weekends. This demonstrates why grouped validation is conservative.

## Technical Details

### 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:

```{r custom_threshold, eval=FALSE}
# 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:

```{r truncation, eval=FALSE}
# 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.

## Summary and Recommendations

### 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