# Specify and fit model using count data from traditional, non eDNA surveys

Source:`R/traditionalModel.R`

`traditionalModel.Rd`

This function implements a Bayesian model that estimates expected species
catch rate using count data from traditional, non eDNA surveys. When
multiple traditional gear types are used, an optional variation allows
estimation of gear scaling coefficients, which scale the catchability of
gear types relative to the expected catch rate of a reference gear type.
Model is implemented using Bayesian inference using the `rstan`

package,
which uses Hamiltonian Monte Carlo to simulate the posterior distributions.
See more examples in the
Package
Vignette.

## Usage

```
traditionalModel(
data,
family = "poisson",
q = FALSE,
phipriors = NULL,
multicore = FALSE,
initial_values = NULL,
n.chain = 4,
n.iter.burn = 500,
n.iter.sample = 2500,
thin = 1,
adapt_delta = 0.9,
verbose = TRUE,
seed = NULL
)
```

## Arguments

- data
A list containing data necessary for model fitting. Valid tags are

`count`

and`count.type`

.`count`

is a matrix or data frame of traditional survey count data, with first dimension equal to the number of sites (i) and second dimension equal to the maximum number of traditional survey replicates at a given site (j).`count.type`

is an optional matrix or data frame of integers indicating gear type (k) used in corresponding count data, with first dimension equal to the number of sites (i) and second dimension equal to the maximum number of traditional survey replicates at a given site (j). Values should be integers beginning with 1 (referring to the first gear type) to n (last gear type). Empty cells should be NA and will be removed during processing. Sites, i, should be consistent in all count data.- family
The distribution class used to model traditional survey count data. Options include poisson ('poisson'), negative binomial ('negbin'), and gamma ('gamma'). Default value is 'poisson'.

- q
A logical value indicating whether to estimate gear scaling coefficients, q, for traditional survey gear types (TRUE) or to not estimate gear scaling coefficients, q, for traditional survey gear types (FALSE). Default value is FALSE.

- phipriors
A numeric vector indicating gamma distribution hyperparameters (shape, rate) used as the prior distribution for phi, the overdispersion in the negative binomial distribution for traditional survey gear data. Used when family = 'negbin.' If family = 'negbin', then default vector is c(0.25,0.25), otherwise, default is NULL.

- multicore
A logical value indicating whether to parallelize chains with multiple cores. Default is FALSE.

- initial_values
A list of lists of initial values to use in MCMC. The length should equal the number of MCMC chains. Initial values can be provided for parameters: mu and q. If no initial values are provided, default random values are drawn.

- n.chain
Number of MCMC chains. Default value is 4.

- n.iter.burn
Number of warm-up MCMC iterations. Default value is 500.

- n.iter.sample
Number of sampling MCMC iterations. Default value is 2500.

- thin
A positive integer specifying the period for saving samples. Default value is 1.

- adapt_delta
Numeric value between 0 and 1 indicating target average acceptance probability used in

`rstan::sampling`

. Default value is 0.9.- verbose
Logical value controlling the verbosity of output (i.e., warnings, messages, progress bar). Default is TRUE.

- seed
A positive integer seed used for random number generation in MCMC. Default is NULL, which means the seed is generated from 1 to the maximum integer supported by R.

## Value

A list of:

a model object of class

`stanfit`

returned by`rstan::sampling`

initial values used in MCMC

## Note

Before fitting the model, this function checks to ensure that the model specification is possible given the data files. These checks include:

All tags in data are valid (i.e., include count and count.type).

Number of sites in count and count type data are equal.

All data are numeric (i.e., integer or NA).

Empty data cells (NA) match in count and count.type.

family is 'poisson', 'negbin', or 'gamma'.

phipriors (if used) is a vector of two numeric values.

If any of these checks fail, the function returns an error message.

## Examples

```
# \donttest{
# Load data
data(greencrabData)
# Examine data in list
# This function uses only traditional survey count data and optionally
# the count type data
names(greencrabData)
#> [1] "qPCR.N" "qPCR.K" "count" "count.type"
# Note that the surveyed sites (rows) should match in the data
dim(greencrabData$count)[1]
#> [1] 20
dim(greencrabData$count.type)[1]
#> [1] 20
# Fit a model without estimating a gear scaling coefficient for traditional
# survey gear types.
# This model assumes all traditional survey methods have the same
# catchability.
# Count data is modeled using a poisson distribution.
fit.no.q <- traditionalModel(data = greencrabData, family = "poisson",
q = FALSE, phipriors = NULL, multicore = FALSE,
verbose = TRUE)
#>
#> SAMPLING FOR MODEL 'traditional_pois' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 5.1e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.51 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 1: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 1: Iteration: 501 / 3000 [ 16%] (Sampling)
#> Chain 1: Iteration: 1000 / 3000 [ 33%] (Sampling)
#> Chain 1: Iteration: 1500 / 3000 [ 50%] (Sampling)
#> Chain 1: Iteration: 2000 / 3000 [ 66%] (Sampling)
#> Chain 1: Iteration: 2500 / 3000 [ 83%] (Sampling)
#> Chain 1: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 0.674 seconds (Warm-up)
#> Chain 1: 1.954 seconds (Sampling)
#> Chain 1: 2.628 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'traditional_pois' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 4.9e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.49 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
#> Chain 2:
#> Chain 2: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 2: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 2: Iteration: 501 / 3000 [ 16%] (Sampling)
#> Chain 2: Iteration: 1000 / 3000 [ 33%] (Sampling)
#> Chain 2: Iteration: 1500 / 3000 [ 50%] (Sampling)
#> Chain 2: Iteration: 2000 / 3000 [ 66%] (Sampling)
#> Chain 2: Iteration: 2500 / 3000 [ 83%] (Sampling)
#> Chain 2: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 2:
#> Chain 2: Elapsed Time: 0.758 seconds (Warm-up)
#> Chain 2: 1.806 seconds (Sampling)
#> Chain 2: 2.564 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'traditional_pois' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 6e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.6 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3:
#> Chain 3:
#> Chain 3: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 3: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 3: Iteration: 501 / 3000 [ 16%] (Sampling)
#> Chain 3: Iteration: 1000 / 3000 [ 33%] (Sampling)
#> Chain 3: Iteration: 1500 / 3000 [ 50%] (Sampling)
#> Chain 3: Iteration: 2000 / 3000 [ 66%] (Sampling)
#> Chain 3: Iteration: 2500 / 3000 [ 83%] (Sampling)
#> Chain 3: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 3:
#> Chain 3: Elapsed Time: 0.671 seconds (Warm-up)
#> Chain 3: 2.008 seconds (Sampling)
#> Chain 3: 2.679 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'traditional_pois' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 4.9e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.49 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4:
#> Chain 4:
#> Chain 4: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 4: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 4: Iteration: 501 / 3000 [ 16%] (Sampling)
#> Chain 4: Iteration: 1000 / 3000 [ 33%] (Sampling)
#> Chain 4: Iteration: 1500 / 3000 [ 50%] (Sampling)
#> Chain 4: Iteration: 2000 / 3000 [ 66%] (Sampling)
#> Chain 4: Iteration: 2500 / 3000 [ 83%] (Sampling)
#> Chain 4: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 4:
#> Chain 4: Elapsed Time: 0.711 seconds (Warm-up)
#> Chain 4: 1.768 seconds (Sampling)
#> Chain 4: 2.479 seconds (Total)
#> Chain 4:
# Fit a model estimating a gear scaling coefficient for traditional survey
# gear types.
# This model does not assume all traditional survey methods have the same
# catchability.
# Count data is modeled using a negative binomial distribution.
fit.q <- traditionalModel(data = greencrabData, family = "negbin", q = TRUE,
phipriors = c(0.25,0.25), multicore = FALSE,
initial_values = NULL, n.chain = 4,
n.iter.burn = 500, n.iter.sample = 2500, thin = 1,
adapt_delta = 0.9, verbose = TRUE, seed = 123)
#>
#> SAMPLING FOR MODEL 'traditional_catchability_negbin' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.000275 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 2.75 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 1: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 1: Iteration: 501 / 3000 [ 16%] (Sampling)
#> Chain 1: Iteration: 1000 / 3000 [ 33%] (Sampling)
#> Chain 1: Iteration: 1500 / 3000 [ 50%] (Sampling)
#> Chain 1: Iteration: 2000 / 3000 [ 66%] (Sampling)
#> Chain 1: Iteration: 2500 / 3000 [ 83%] (Sampling)
#> Chain 1: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 3.555 seconds (Warm-up)
#> Chain 1: 7.965 seconds (Sampling)
#> Chain 1: 11.52 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'traditional_catchability_negbin' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 0.000313 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 3.13 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
#> Chain 2:
#> Chain 2: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 2: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 2: Iteration: 501 / 3000 [ 16%] (Sampling)
#> Chain 2: Iteration: 1000 / 3000 [ 33%] (Sampling)
#> Chain 2: Iteration: 1500 / 3000 [ 50%] (Sampling)
#> Chain 2: Iteration: 2000 / 3000 [ 66%] (Sampling)
#> Chain 2: Iteration: 2500 / 3000 [ 83%] (Sampling)
#> Chain 2: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 2:
#> Chain 2: Elapsed Time: 3.643 seconds (Warm-up)
#> Chain 2: 9.884 seconds (Sampling)
#> Chain 2: 13.527 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'traditional_catchability_negbin' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 0.000269 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 2.69 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3:
#> Chain 3:
#> Chain 3: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 3: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 3: Iteration: 501 / 3000 [ 16%] (Sampling)
#> Chain 3: Iteration: 1000 / 3000 [ 33%] (Sampling)
#> Chain 3: Iteration: 1500 / 3000 [ 50%] (Sampling)
#> Chain 3: Iteration: 2000 / 3000 [ 66%] (Sampling)
#> Chain 3: Iteration: 2500 / 3000 [ 83%] (Sampling)
#> Chain 3: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 3:
#> Chain 3: Elapsed Time: 3.567 seconds (Warm-up)
#> Chain 3: 8.463 seconds (Sampling)
#> Chain 3: 12.03 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'traditional_catchability_negbin' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 0.000317 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 3.17 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4:
#> Chain 4:
#> Chain 4: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 4: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 4: Iteration: 501 / 3000 [ 16%] (Sampling)
#> Chain 4: Iteration: 1000 / 3000 [ 33%] (Sampling)
#> Chain 4: Iteration: 1500 / 3000 [ 50%] (Sampling)
#> Chain 4: Iteration: 2000 / 3000 [ 66%] (Sampling)
#> Chain 4: Iteration: 2500 / 3000 [ 83%] (Sampling)
#> Chain 4: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 4:
#> Chain 4: Elapsed Time: 3.296 seconds (Warm-up)
#> Chain 4: 7.634 seconds (Sampling)
#> Chain 4: 10.93 seconds (Total)
#> Chain 4:
# }
```