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Specify and fit joint model using count data from traditional surveys and eDNA PCR data

Source: R/joint_model.R
joint_model.Rd

This function implements a Bayesian model that integrates data from paired eDNA and traditional surveys, as described in Keller et al. (2022) <doi.org/10.1002/eap.2561>. The model estimates parameters including the expected species catch rate and the probability of false positive eDNA detection. This function allows for optional model variations, like inclusion of site-level covariates that scale the sensitivity of eDNA sampling relative to traditional sampling, as well as estimation of gear scaling coefficients that scales the relative catchability of multiple traditional gear types. 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

joint_model(
  data,
  cov = NULL,
  family = "poisson",
  p10_priors = c(1, 20),
  q = FALSE,
  phi_priors = NULL,
  multicore = FALSE,
  initial_values = NULL,
  n_chain = 4,
  n_warmup = 500,
  n_iter = 3000,
  thin = 1,
  adapt_delta = 0.9,
  verbose = TRUE,
  seed = NULL
)

Arguments

data

A list containing data necessary for model fitting. Valid tags are pcr_n, pcr_k, count, count_type, and site_cov. pcr_n and pcr_k are matrices or data frames with first dimension equal to the number of sites (i) and second dimension equal to the maximum number of eDNA samples at a given site (m). pcr_n contains the total number of PCR replicates per site and eDNA sample, and pcr_k contains the total number of positive PCR detections per site and eDNA sample. 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 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. Values should be integers beginning with 1 (referring to the first gear type) to n (last gear type). site_cov is an optional matrix or data frame of site-level covariate data, with first dimension equal to the number of sites (i). site_cov should include informative column names. Empty cells should be NA and will be removed during processing. Sites, i, should be consistent in all PCR, count, and site covariate data.

cov

A character vector indicating the site-level covariates to include in the model. Default value is NULL.

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'.

p10_priors

A numeric vector indicating beta distribution hyperparameters (alpha, beta) used as the prior distribution for the eDNA false positive probability (p10). Default vector is c(1,20).

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.

phi_priors

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: beta, p10 (log-scale), mu, q, alpha. If no initial values are provided, default random values are drawn.

n_chain

Number of MCMC chains. Default value is 4.

n_warmup

A positive integer specifying the number of warm-up MCMC iterations. Default value is 500.

n_iter

A positive integer specifying the number of iterations for each chain (including warmup). Default value is 3000.

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 pcr_n, pcr_k, count, count_type, and site_cov).

  • Dimensions of pcr_n and pcr_k are equal, and dimensions of count and count_type are equal (if count_type provided).

  • Number of sites in PCR and count data are equal.

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

  • Empty data cells (NA) match in pcr_n and pcr_k and in count and count_type.

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

  • p10_priors and phi_priors (if used) is a vector of two numeric values.

  • site_cov has same number of rows as pcr_n and count, if present

  • site_cov is numeric, if present

  • cov values match column names in site_cov, if present

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

Examples

# \donttest{
# Ex. 1: Implementing the joint model

# Load data
data(goby_data)

# Examine data in list
names(goby_data)
#> [1] "pcr_n"    "pcr_k"    "count"    "site_cov"

# Note that the surveyed sites (rows) should match in all data
dim(goby_data$pcr_n)[1]
#> [1] 39
dim(goby_data$count)[1]
#> [1] 39

# Fit a basic model with paired eDNA and traditional survey data.
# Count data is modeled using a poisson distribution.
fit <- joint_model(data = goby_data, family = "poisson",
                   p10_priors = c(1, 20),
                   multicore = FALSE)
#> 
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 4.9e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.49 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: 0.903 seconds (Warm-up)
#> Chain 1:                1.661 seconds (Sampling)
#> Chain 1:                2.564 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 4.8e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.48 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)
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#> 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: 0.946 seconds (Warm-up)
#> Chain 2:                1.67 seconds (Sampling)
#> Chain 2:                2.616 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 4.4e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.44 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)
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#> Chain 3: Iteration: 2500 / 3000 [ 83%]  (Sampling)
#> Chain 3: Iteration: 3000 / 3000 [100%]  (Sampling)
#> Chain 3: 
#> Chain 3:  Elapsed Time: 0.967 seconds (Warm-up)
#> Chain 3:                1.679 seconds (Sampling)
#> Chain 3:                2.646 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 4.4e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.44 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: 0.88 seconds (Warm-up)
#> Chain 4:                1.648 seconds (Sampling)
#> Chain 4:                2.528 seconds (Total)
#> Chain 4: 
#> Refer to the eDNAjoint guide for visualization tips:  https://ednajoint.netlify.app/tips#visualization-tips 

# Ex. 2: Implementing the joint model with site-level covariates

# With the same data, fit a model including 'Filter_time' and 'Salinity'
# site-level covariates
# These covariates will scale the sensitivity of eDNA sampling relative to
# traditional surveys
# Count data is modeled using a poisson distribution.
fit_cov <- joint_model(data = goby_data, cov = c('Filter_time','Salinity'),
                       family = "poisson", p10_priors = c(1, 20),
                       multicore = FALSE)
#> 
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 4.9e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.49 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: 0.871 seconds (Warm-up)
#> Chain 1:                1.68 seconds (Sampling)
#> Chain 1:                2.551 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 4.3e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.43 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: 4.615 seconds (Warm-up)
#> Chain 2:                1.642 seconds (Sampling)
#> Chain 2:                6.257 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 5.5e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.55 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)
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#> Chain 3: Iteration: 3000 / 3000 [100%]  (Sampling)
#> Chain 3: 
#> Chain 3:  Elapsed Time: 0.572 seconds (Warm-up)
#> Chain 3:                1.653 seconds (Sampling)
#> Chain 3:                2.225 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 6.5e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.65 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)
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#> 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: 0.898 seconds (Warm-up)
#> Chain 4:                1.681 seconds (Sampling)
#> Chain 4:                2.579 seconds (Total)
#> Chain 4: 
#> Refer to the eDNAjoint guide for visualization tips:  https://ednajoint.netlify.app/tips#visualization-tips 


# Ex. 3: Implementing the joint model with multiple traditional gear types

# Load data
data(green_crab_data)

# Examine data in list
names(green_crab_data)
#> [1] "pcr_n"      "pcr_k"      "count"      "count_type"

# Note that the surveyed sites (rows) should match in all data
dim(green_crab_data$pcr_n)[1]
#> [1] 20
dim(green_crab_data$count)[1]
#> [1] 20

# 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 <- joint_model(data = green_crab_data, cov = NULL, family = "negbin",
                     p10_priors = c(1, 20), q = TRUE,
                     phi_priors = c(0.25, 0.25),
                     multicore = FALSE, initial_values = NULL,
                     n_chain = 4, n_warmup = 500,
                     n_iter = 3000, thin = 1, adapt_delta = 0.9,
                     verbose = TRUE, seed = 123)
#> 
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 0.000314 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 3.14 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: 3.744 seconds (Warm-up)
#> Chain 1:                9.715 seconds (Sampling)
#> Chain 1:                13.459 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 0.000352 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 3.52 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)
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#> Chain 2: Iteration: 2500 / 3000 [ 83%]  (Sampling)
#> Chain 2: Iteration: 3000 / 3000 [100%]  (Sampling)
#> Chain 2: 
#> Chain 2:  Elapsed Time: 3.823 seconds (Warm-up)
#> Chain 2:                8.543 seconds (Sampling)
#> Chain 2:                12.366 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 0.000351 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 3.51 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)
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#> Chain 3: Iteration: 2500 / 3000 [ 83%]  (Sampling)
#> Chain 3: Iteration: 3000 / 3000 [100%]  (Sampling)
#> Chain 3: 
#> Chain 3:  Elapsed Time: 3.988 seconds (Warm-up)
#> Chain 3:                12.6 seconds (Sampling)
#> Chain 3:                16.588 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 0.000343 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 3.43 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)
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#> Chain 4: Iteration: 2500 / 3000 [ 83%]  (Sampling)
#> Chain 4: Iteration: 3000 / 3000 [100%]  (Sampling)
#> Chain 4: 
#> Chain 4:  Elapsed Time: 3.877 seconds (Warm-up)
#> Chain 4:                10.499 seconds (Sampling)
#> Chain 4:                14.376 seconds (Total)
#> Chain 4: 
#> Refer to the eDNAjoint guide for visualization tips:  https://ednajoint.netlify.app/tips#visualization-tips 
# }