--- title: "Bus-Route Surveys" output: rmarkdown::html_vignette: highlight: null vignette: > %\VignetteIndexEntry{Bus-Route Surveys} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r setup, include = FALSE} knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) ``` ## What is a Bus-Route Survey? A bus-route survey visits multiple access points (sites) in a fixed route, called a circuit. Unlike an access-point creel survey that stations an interviewer at one location for the day, a bus-route crew travels the circuit repeatedly, counting and interviewing anglers at each site as they pass through. Sites are not weighted equally. The crew visits every site on each pass but waits longer at busier sites (Jones & Pollock 2012, Box 19.3), so a party at a busy site is more likely to be seen. A site's weight is the share of the circuit the crew spends there: its wait divided by the time to complete the whole circuit, travel included (Robson & Jones 1989; Pollock et al. 1994, eq. 15.10). Inverse weighting by that share is what makes the estimate unbiased. Two types of data are collected during each visit: - **Enumeration counts** — every angler party at the site is counted (`n_counted`). - **Interviews** — a subset of parties is interviewed to collect effort and catch data (`n_interviewed`). The ratio `n_counted / n_interviewed` (the enumeration expansion factor) scales the interviewed catch and effort up to represent all parties at the site, including those not interviewed. Without this expansion, busy sites are systematically underrepresented in the total estimate. The estimator is the bus-route design of Robson & Jones (1989), as set out in Pollock et al. (1994, section 15.5.3). It is written in the general Horvitz-Thompson form of Jones & Pollock (2012, Chapter 19). ## Key Concepts ### Inclusion Probability (πᵢ) The inclusion probability πᵢ is the probability that a given sampling unit (site × period combination) is included in the sample. For a two-stage bus-route design: $$\pi_i = p\_site_i \times p\_period$$ where `p_period` is the probability that the period containing the visit is sampled, and `p_site` is the site's weight within the circuit. It can be given in two ways: - **`wait_time` and `circuit_time`**, for a route that visits every site on each pass. `p_site` is then `wait_time / circuit_time`. These shares add up to less than 1 whenever the route has travel time, and that is correct: no party can be seen while the crew is driving. - **`p_site`**, the probability that a pass selects the site, for a design in which each pass visits a randomly chosen site. These probabilities add up to 1 within a circuit. Do not rescale wait times so that they add up to 1. That divides by the total wait rather than the circuit time, and every total comes out too low by the share of the circuit spent travelling. The inclusion probability πᵢ belongs to the *sampling design*, not to a site or its anglers. Specify it when designing the survey; do not compute it from the interview data. ### Enumeration Counts During each circuit pass, the crew counts every visible angler party at the site (`n_counted`) and then interviews as many as possible (`n_interviewed`). When not all parties are interviewed, the expansion factor $$\text{expansion} = \frac{n\_counted}{n\_interviewed}$$ rescales the interviewed data so it represents all parties. If all parties are interviewed (n_counted = n_interviewed), the expansion is 1 and no adjustment is needed, as in the example below. ### Horvitz-Thompson Estimator The total effort estimator (Jones & Pollock 2012, Eq. 19.4) is: $$\hat{E} = \sum_i \frac{e_i}{\pi_i}$$ where $e_i = \text{hours\_fished}_i \times \text{expansion}_i$ is the enumeration-expanded effort for interview _i_. Each site's contribution is weighted by the reciprocal of its inclusion probability. A site sampled with probability 0.20 receives weight 5 — five times the weight of a site sampled with probability 1.0. This inverse-probability weighting is what makes the estimator statistically unbiased. The harvest estimator (Jones & Pollock 2012, Eq. 19.5) follows the same structure: $$\hat{H} = \sum_i \frac{h_i}{\pi_i}$$ ## Choosing the Site Weights Some implementations fix $\pi_i = 0.5$ for every site. That is not an inclusion probability of the design, and each site's contribution is then off by the ratio of 0.5 to its true $\pi_i$. tidycreel computes $\pi_i = p\_site \times p\_period$ from the sampling frame you give `creel_design()`, with `p_site` either supplied directly or computed as `wait_time / circuit_time`. The test suite reproduces the bus-route effort and catch examples in Pollock et al. (1994, Tables 15.16 and 15.17) from wait and circuit times. Malvestuto (1996, Box 20.6) uses the same inverse-probability rule in its access-point and roving examples, and the test suite reproduces its Examples 1 and 2. ## Step-by-Step Example We demonstrate the full bus-route workflow on a small constructed example: a four-site, single-circuit survey with 15 interviews over four days. The numbers are invented, so the totals below are this example's own arithmetic, not published figures. The test suite checks the same estimator against a published example, Pollock et al. (1994, Tables 15.16 and 15.17); the [equations page](bus-route-equations.html) works through it. ### Step 1: Define the Sampling Design The sampling frame lists the four sites, the crew's scheduled wait at each, and the time to drive the whole circuit once, waits included: 400 minutes, of which 200 are waits and 200 are travel. Each day the crew works either the morning or the afternoon, chosen with equal probability, so `p_period = 0.5`. ```{r design} library(tidycreel) # Sampling frame: 4 sites, 1 circuit. Waits are longer at busier sites. sampling_frame <- data.frame( site = c("A", "B", "C", "D"), circuit = "circ1", wait_min = c(60, 50, 80, 10), # 200 min of waits circuit_min = 400, # whole circuit, travel included p_period = 0.50 # morning or afternoon, equally likely ) # Site weight: p_site = wait / circuit time; pi_i = p_site * p_period # Site A: 60 / 400 = 0.150; x 0.5 = 0.0750 # Site B: 50 / 400 = 0.125; x 0.5 = 0.0625 # Site C: 80 / 400 = 0.200; x 0.5 = 0.1000 # Site D: 10 / 400 = 0.025; x 0.5 = 0.0125 # Survey calendar: 4 weekdays calendar <- data.frame( date = as.Date(c("2024-06-01", "2024-06-02", "2024-06-03", "2024-06-04")), day_type = "weekday" ) # Build the bus-route design design <- creel_design( calendar, date = date, strata = day_type, survey_type = "bus_route", sampling_frame = sampling_frame, site = site, circuit = circuit, wait_time = wait_min, circuit_time = circuit_min, p_period = p_period ) print(design) ``` The design object stores the sampling frame and precomputes πᵢ for each site×circuit combination. The four site shares add up to 0.5, not 1: half the circuit is spent driving, when no party can be seen. Site C has the longest wait and therefore the highest πᵢ (0.10), so each of its parties stands for fewer unseen ones than a party at Site D (πᵢ = 0.0125). ### Step 2: Attach Interview Data Each row of interview data represents one interviewed party. The `n_counted` and `n_interviewed` columns record how many parties were at the site vs. how many were actually interviewed. In this example both are equal (no expansion needed), but the columns must still be supplied for bus-route designs. Each party's effort is recorded here as angler-hours: the hours fished times the number of anglers in the party. Because the column already counts every angler, `n_anglers = 1` tells `add_interviews()` to take each value as it stands. If your sheet records hours per party and party size separately, pass the hours as `effort` and the party size as `n_anglers` instead, and tidycreel multiplies them. ```{r interviews} # 15 interviews across 4 sites and 4 days # Site A: 4 interviews (all 4 parties interviewed) # Site B: 3 interviews (all 3 parties) # Site C: 6 interviews (all 6 parties) — highest effort site # Site D: 2 interviews (all 2 parties) interviews_raw <- data.frame( date = as.Date(c( "2024-06-01", "2024-06-01", "2024-06-02", "2024-06-02", # Site A "2024-06-01", "2024-06-02", "2024-06-03", # Site B "2024-06-01", "2024-06-02", "2024-06-03", # Site C (rows 1-3) "2024-06-03", "2024-06-04", # Site C (rows 4-5) "2024-06-03", "2024-06-04", # Site D "2024-06-03" # Site C (row 6) )), day_type = "weekday", site = c( "A", "A", "A", "A", "B", "B", "B", "C", "C", "C", "C", "C", "D", "D", "C" ), circuit = "circ1", angler_hours = c( 7.5, 7.5, 7.5, 7.5, # Site A: 4 x 7.5 = 30 h total 20.0 / 3, 20.0 / 3, 20.0 / 3, # Site B: 3 x 6.67 = 20 h total 57.5 / 6, 57.5 / 6, 57.5 / 6, # Site C rows 1-3 57.5 / 6, 57.5 / 6, # Site C rows 4-5 2.5, 2.5, # Site D: 2 x 2.5 = 5 h total 57.5 / 6 # Site C row 6: total = 57.5 h ), fish_kept = c( 1L, 0L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L ), fish_caught = c( 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L ), n_counted = c( 4L, 4L, 4L, 4L, 3L, 3L, 3L, 6L, 6L, 6L, 6L, 6L, 2L, 2L, 6L ), n_interviewed = c( 4L, 4L, 4L, 4L, 3L, 3L, 3L, 6L, 6L, 6L, 6L, 6L, 2L, 2L, 6L ), trip_status = "complete" ) # Attach interviews — pi_i is joined automatically from the sampling frame design <- add_interviews( design, interviews_raw, effort = angler_hours, catch = fish_caught, harvest = fish_kept, n_counted = n_counted, n_interviewed = n_interviewed, trip_status = trip_status, n_anglers = 1 ) print(design) ``` `add_interviews()` joins πᵢ from the sampling frame to each interview row (stored as `.pi_i`) and computes the enumeration expansion factor (`.expansion = n_counted / n_interviewed`). These are used internally by the estimation functions. ### Step 3: Estimate Effort `estimate_effort()` dispatches to the bus-route estimator and computes $\hat{E} = \sum(e_i / \pi_i)$. ```{r effort} # Estimate total angler-hours effort_est <- estimate_effort(design) print(effort_est) # Inspect per-site contributions to the total site_contribs <- get_site_contributions(effort_est) print(site_contribs) ``` The site contributions table shows exactly how each site's effort feeds into the total. Site C (πᵢ = 0.10, observed effort 57.5 h) contributes 57.5 / 0.10 = 575 angler-hours, the largest single-site contribution. Site D (πᵢ = 0.0125, observed effort 5 h) contributes 5 / 0.0125 = 400 angler-hours: the crew waits there for only 10 minutes of each 400, so each party seen stands for many that were not. The total is over the four sampled days. Bus-route totals refuse `target = "stratum_total"` and `"period_total"` (the expansion to unsampled days is not implemented). ### Step 4: Estimate Catch and Harvest `estimate_harvest_rate()` gives fish kept per angler-hour. The totals apply the same Horvitz-Thompson logic as effort, dividing each party's fish by its inclusion probability and summing. ```{r harvest} # Fish kept per angler-hour harvest_rate <- estimate_harvest_rate(design) print(harvest_rate) # Total fish kept (harvest) and total fish caught (kept + released) harvest_est <- estimate_total_harvest(design) print(harvest_est) catch_est <- estimate_total_catch(design) print(catch_est) ``` ### Step 5: Results as Data Each estimate converts to a tibble with its method, variance method and unit as columns, ready for `dplyr` or a report table, and plots with its confidence interval: ```{r results, fig.width = 6, fig.height = 3, fig.alt = "Total catch estimate with its 95 percent confidence interval."} tibble::as_tibble(catch_est) ggplot2::autoplot(catch_est) ``` ## Checking the Arithmetic Each site contributes its observed effort divided by its inclusion probability: | Site | wait / circuit | πᵢ | e_i (h) | e_i / πᵢ | |------|----------------|--------|---------|----------| | A | 60 / 400 | 0.0750 | 30.0 | 400 | | B | 50 / 400 | 0.0625 | 20.0 | 320 | | C | 80 / 400 | 0.1000 | 57.5 | 575 | | D | 10 / 400 | 0.0125 | 5.0 | 400 | | **Total** | | | | **1,695** | Rescaling the waits to add up to 1 (60/200, 50/200, ...) would have given 847.5, half the total, because half the circuit is travel. That is the error the `wait_time` and `circuit_time` arguments exist to prevent. ## References - Jones, C. M., & Pollock, K. H. (2012). Recreational angler survey methods: estimation of effort, harvest, and released catch. Chapter 19 in *Fisheries Techniques* (3rd ed.), pp. 883–919. American Fisheries Society. - Malvestuto, S. P. (1996). Sampling the recreational creel. Chapter 20 in *Fisheries Techniques* (2nd ed.), pp. 591–623. American Fisheries Society. - Pollock, K. H., Jones, C. M., & Brown, T. L. (1994). *Angler survey methods and their applications in fisheries management*. American Fisheries Society Special Publication 25. - Robson, D., & Jones, C. M. (1989). The theoretical basis of an access site angler survey design. *Biometrics*, 45, 83–98.