Estimation Methods

Basic Estimation Methods

The MRIP catch and effort estimates are produced using information from three complementary surveys.

• The Coastal Household Telephone Survey (CHTS) of private households is used to monitor the number of fishing days for shore and private boat fishermen. The CHTS collects fishing activity data that can be used to estimate the total number of shore and private mode angler trips (effort).
• The For-Hire Survey (FHS) is a telephone survey of for-hire boat operators that is used to monitor the number of day trips made by fishermen using charter boats and head/party boats. The FHS collects fishing activity data that can be used to estimate the total number of charter/head boat angler trips (effort). Additionally, the Southeast Region Headboat Survey samples and monitors the recreational headboat fishery in the south Atlantic and Gulf of Mexico.
• The Access Point Angler Intercept Survey (APAIS) is a survey at fishing/marina sites that monitors the catch rates of fishing participants in the shore, private boat, and charter boat modes. The APAIS collects data that are used to estimate catch by species per angler fishing trip. The APAIS interviews are completed on-site and in-person by trained interviewers. In the Northeast, catch rate for head boats is determined from the observations of at-sea samplers who monitor catch aboard sampled head boat trips.

We calculate effort through the two telephone surveys and average trip catch rates through the on-site APAIS interviews. The effort estimate can be used to expand the mean catch rate to get an estimate of the total number of fish caught.

Effort x Catch Rate = Total Catch

For example, if 5 people made 3 trips each (15 angler trips total) and averaged one black sea bass and two cod per trip, we would estimate their total catch to be:

15 angler trips x 1 black sea bass per trip = 15 black sea bass

15 angler trips x 2 cod per trip = 30 cod

We produce estimates for every species, every type of fishing (mode), and three different catch types. 1) Type A catch estimates are based on fish brought back to the dock and observed and identified by trained interviewers. 2) Type B1 catch estimates are based on reported fish that were used for bait, released dead, or filleted ( i.e. they are killed but identification is by individual anglers and not samplers). 3) Type B2 catch estimates are based on reported fish that were released alive (again, identification is by individual anglers).

This is the most fundamental approach to estimating total catch. However, it is usually necessary to make adjustments to the effort estimates produced by the CHTS and FHS. For example, the CHTS only samples coastal households and therefore does not reach people in inland states. We use information from the on-site APAIS survey, where we ask what state a person is from, to adjust the estimates accordingly. A similar adjustment is made for the FHS charter angler trip estimate to account for angler fishing trips on charter boats not included in that survey (it's voluntary).

Example: Basic Estimation with Effort Adjustment

The following table is an example of the various components from the complementary surveys that are used to generate catch estimates for private boat mode in Massachusetts. Use the numbers in the table below to follow these steps to estimate catch estimates:

1. Start with the original estimated private boat mode effort for Massachusetts from the CHTS for two-month sample intervals Waves 3 (May-June), 4 (July-August), and 5 (September-October) for the years 2011, 2012, and 2013.
2. Calculate the coverage adjustment factor (Adjustment on the table, accounts for people not able to be surveyed) for that wave, and multiply it by the original effort to get an adjusted effort estimate.
3. Calculate the weighted mean catch per angler trip (Catch Per Effort on the table) from the APAIS survey (for private boat mode, in this case)
4. Multiply the adjusted effort estimate of angler trips by the catch per trip estimate to obtain the catch estimate.

Weighting Estimation

In the basic estimation example, we indicate that we obtain a weighted estimate of the mean catch per angler trip from the APAIS data. Per standard survey design methodology, survey weights account for the fact that some people and sites are more likely to have interviews than others . If we did not try to account for this, our estimates would be less accurate. For basic weighting, if a given sample unit had a 1/10 chance of being selected, the assigned weight would be the inverse of that probability, or 10/1 = 10. In the APAIS, there are multiple stages of sample selection that require weighting . An example is provided below to clarify how this is done. The following numbers are for illustrative purposes only, and do not represent actual numbers used in our survey estimates.

Primary Stage Weights
The first sampling unit for the APAIS is a specific fishing site and time interval. The probability of selection for a given site-time combination depends on how active the fishing site is expected to be during the time interval, as predicted from historical information. For example, let's say that we have three types of fishing sites and their expected activity during an assigned time interval for interviewing:

L for low activity, expected to have about 10 angler trips

M for medium activity,expected to have about 40 angler trips

H for high activity, expected to have about 100 angler trips

Let's say for a given area we have 40 L-sites, 20 M-sites, and 8 H-sites. Based on the known activity levels, the probability of selection for each site is:

probability of selection for a given site-time combination =
activity level (L, M, or H) / (L*L-sites + M*M-sites + H*H-sites)

L-sites: each site has a 1/200 chance of being selected (10 / (10*40+40*20+100*8)=1/200)

M-sites: each site has a 1/50 chance of being selected (40 / (10*40+40*20+100*8)=1/50)

H-sites: each site has a 1/20 chance of being selected (100 / (10*40+40*20+100*8)=1/20)

Now, let's say we take a small sample of 5 site-days and end up selecting 1 L-site, 2 M-sites, and 2 H-sites. The site weights are the inverse of the selection probabilities, so in this example the primary stage weights for L-sites would be 200, M-site weights would be 50, and H-site weights would be 20.

Secondary Stage Weights
When visiting an assigned site in an assigned time interval, each APAIS interviewer tries to interview as many anglers who have completed fishing for the day as he/she can while keeping track of how many total trips were completed at the site. For the lower activity sites, it may be easy to interview every angler trip, while at the higher activity sites, people may be leaving at the same time and the interviewer may not be able to interview every angler. For each assignment, we calculate a second stage selection probability, and also create a weight for each interview that is based on the inverse of that probability.

Working with our example:

At the L-site, there were 10 trips as expected and all 10 were interviewed, so the probability is 10/10, or 1 and the weight is also 1.

At the M-sites, there were 40 trips but only 32 were interviewed, so the probability is 32/40 = 4/5, and the weight is 5/4 = 1.25.

At the H-sites, there were 100 trips but only 40 were interviewed, so the probability of selection is 40/100 = 2/5, and the weight is 5/2 = 2.5.

Combining Weights
The overall weights assigned to each trip can then be calculated by multiplying the site-time-selection (primary stage) weight by the trip-selection (secondary stage) weight. The overall weights assigned to each trip in our example are:

L-sites: 200*1 = 200

M-sites: 50*1.25 = 62.5

H-sites: 20*2.5 = 50

Calculating Catch per Unit Effort

To calculate the weighted catch per unit effort for a particular species, we sum the product of the number of fish caught by the respective trip weight and then divide by the total sum of the weights themselves. This produces a weighted average that correctly reflects the sample design. To continue with our example, let's say that we're interested in species X. A the L-site that was selected, a total of 6 fish of species X were caught among the 10 interviewed trips. Across the selected M-sites, a total of 30 fish of species X were caught among the 64 total interviewedtrips. Across the selected H-sites, a total of 34 fish of species X were caught among the 80 total interviewed trips.

Combining the information above, we can calculate the weighted catch estimate for species X by multiplying the number of fish caught at each site by the appropriate weight and summing them. In this case, the weighted catch estimates are:

L-sites: 6*200 = 1,200

M-sites: 30*62.5 = 1,875

H-sites: 34*50 = 1,700

Sum: 1,200+1,875+1,700 = 4,775

To calculate the weighted catch per unit effort, we need to divide this by the total sum of the weights. We can calculate that by multiplying the combined weights by the total number of interviewed trips for a particular site. In this example, the sum of the weights would be 10*200+64*62.5+80*50=10,000. Therefore, the weighted mean catch per angler trip would be 4,775/10,000=0.4775.

The "unweighted" mean catch per angler trip could be calculated by taking the total number of fish caught and dividing by the total number of interviewed trips, or 70/154=0.4545. However, this is a biased estimate of the actual catch per unit effort because it doesn't reflect the sampling design. This may not look like a large numerical difference from the weighted estimate, but the difference could be much larger for other examples.

Example: Weighted Estimation

The table below shows the weighted estimation example described in the previous tab.  Each of the steps in calculating weighted estimates is demonstrated below.