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: 0.422 seconds (Warm-up)
#> Chain 1: 0.869 seconds (Sampling)
#> Chain 1: 1.291 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 2.7e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.27 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: 0.379 seconds (Warm-up)
#> Chain 2: 0.853 seconds (Sampling)
#> Chain 2: 1.232 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 2.7e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.27 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: 0.42 seconds (Warm-up)
#> Chain 3: 0.863 seconds (Sampling)
#> Chain 3: 1.283 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 2.8e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.28 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: 1.16 seconds (Warm-up)
#> Chain 4: 1.18 seconds (Sampling)
#> Chain 4: 2.34 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] 0.005318584
#>
#> $lower_ci
#> Highest Density Interval: 1.77e-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] 0.004462148
#>
#> $lower_ci
#> Highest Density Interval: 1.43e-03
#>
#> $upper_ci
#> Highest Density Interval: 8.08e-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 0.000395 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 3.95 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: 4.695 seconds (Warm-up)
#> Chain 1: 12.857 seconds (Sampling)
#> Chain 1: 17.552 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 0.000472 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 4.72 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: 5.037 seconds (Warm-up)
#> Chain 2: 16.994 seconds (Sampling)
#> Chain 2: 22.031 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 0.000453 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 4.53 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: 4.832 seconds (Warm-up)
#> Chain 3: 12.485 seconds (Sampling)
#> Chain 3: 17.317 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 0.000467 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 4.67 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: 5.113 seconds (Warm-up)
#> Chain 4: 14.635 seconds (Sampling)
#> Chain 4: 19.748 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
# }