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 3.1e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.31 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: 0.428 seconds (Warm-up)
#> Chain 1: 0.887 seconds (Sampling)
#> Chain 1: 1.315 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: 0.384 seconds (Warm-up)
#> Chain 2: 0.87 seconds (Sampling)
#> Chain 2: 1.254 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 2.6e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.26 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: 0.423 seconds (Warm-up)
#> Chain 3: 0.867 seconds (Sampling)
#> Chain 3: 1.29 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 3.7e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.37 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: 1.158 seconds (Warm-up)
#> Chain 4: 1.179 seconds (Sampling)
#> Chain 4: 2.337 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 0.000598 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 5.98 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: 4.718 seconds (Warm-up)
#> Chain 1: 12.897 seconds (Sampling)
#> Chain 1: 17.615 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 0.000429 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 4.29 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: 5.064 seconds (Warm-up)
#> Chain 2: 17.01 seconds (Sampling)
#> Chain 2: 22.074 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 0.000503 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 5.03 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: 4.844 seconds (Warm-up)
#> Chain 3: 12.502 seconds (Sampling)
#> Chain 3: 17.346 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 0.000438 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 4.38 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: 5.12 seconds (Warm-up)
#> Chain 4: 14.673 seconds (Sampling)
#> Chain 4: 19.793 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
# }