This function uses the full posterior distributions of parameters estimated
by joint_model() to calculate mu_critical, or the expected catch rate at
which the probabilities of a false positive eDNA detection and true positive
eDNA detection are equal. See more examples in the
Package
Vignette.
Value
A list with median mu_critical and lower and upper bounds on the credible interval. If multiple gear types are used, a table of mu_critical and lower and upper credible interval bounds is returned with one column for each gear type.
Note
Before fitting the model, this function checks to ensure that the function is possible given the inputs. These checks include:
Input model fit is an object of class 'stanfit'.
Input credible interval is a univariate numeric value greater than 0 and less than 1.
Input model fit contains p10 parameter.
If model fit contains alpha, cov_val must be provided.
Input cov_val is numeric.
Input cov_val is the same length as the number of estimated covariates.
Input model fit has converged (i.e. no divergent transitions after warm-up).
If any of these checks fail, the function returns an error message.
Examples
# \donttest{
# Ex. 1: Calculating mu_critical with site-level covariates
# Load data
data(goby_data)
# Fit a model including 'Filter_time' and 'Salinity' site-level covariates
fit_cov <- joint_model(data = goby_data, cov = c('Filter_time','Salinity'),
family = "poisson", p10_priors = c(1,20), q = FALSE,
multicore = FALSE)
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 3.2e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.32 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: 0.378 seconds (Warm-up)
#> Chain 1: 0.885 seconds (Sampling)
#> Chain 1: 1.263 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 2.5e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.25 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: 3.191 seconds (Warm-up)
#> Chain 2: 0.885 seconds (Sampling)
#> Chain 2: 4.076 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 2.5e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.25 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: 0.392 seconds (Warm-up)
#> Chain 3: 0.867 seconds (Sampling)
#> Chain 3: 1.259 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 2.5e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.25 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: 0.339 seconds (Warm-up)
#> Chain 4: 0.892 seconds (Sampling)
#> Chain 4: 1.231 seconds (Total)
#> Chain 4:
#> Refer to the eDNAjoint guide for visualization tips: https://ednajoint.netlify.app/tips#visualization-tips
# Calculate mu_critical at the mean covariate values (covariates are
# standardized, so mean = 0)
mu_critical(fit_cov$model, cov_val = c(0,0), ci = 0.9)
#> $median
#> [1] 0.00528536
#>
#> $lower_ci
#> Highest Density Interval: 1.79e-03
#>
#> $upper_ci
#> Highest Density Interval: 9.63e-03
#>
# Calculate mu_critical at habitat size 0.5 z-scores greater than the mean
mu_critical(fit_cov$model, cov_val = c(0,0.5), ci = 0.9)
#> $median
#> [1] 0.004416897
#>
#> $lower_ci
#> Highest Density Interval: 1.56e-03
#>
#> $upper_ci
#> Highest Density Interval: 8.23e-03
#>
# Ex. 2: Calculating mu_critical with multiple traditional gear types
# Load data
data(green_crab_data)
# Fit a model with no site-level covariates
fit_q <- joint_model(data = green_crab_data, cov = NULL, family = "negbin",
p10_priors = c(1,20), q = TRUE, multicore = FALSE)
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.000441 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 4.41 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: 5.059 seconds (Warm-up)
#> Chain 1: 13.496 seconds (Sampling)
#> Chain 1: 18.555 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 0.000465 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 4.65 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: 5.435 seconds (Warm-up)
#> Chain 2: 17.802 seconds (Sampling)
#> Chain 2: 23.237 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 0.000461 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 4.61 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: 5.207 seconds (Warm-up)
#> Chain 3: 13.114 seconds (Sampling)
#> Chain 3: 18.321 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 0.000464 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 4.64 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: 5.525 seconds (Warm-up)
#> Chain 4: 15.356 seconds (Sampling)
#> Chain 4: 20.881 seconds (Total)
#> Chain 4:
#> Refer to the eDNAjoint guide for visualization tips: https://ednajoint.netlify.app/tips#visualization-tips
# Calculate mu_critical
mu_critical(fit_q$model, cov_val = NULL, ci = 0.9)
#> gear_1 gear_2
#> median 0.05962583 0.04601941
#> lower_ci 0.00982894 0.00700122
#> upper_ci 0.13537095 0.10428428
# }