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 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: 0.721 seconds (Warm-up)
#> Chain 1: 1.704 seconds (Sampling)
#> Chain 1: 2.425 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 5.6e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.56 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: 2.34 seconds (Warm-up)
#> Chain 2: 3.826 seconds (Sampling)
#> Chain 2: 6.166 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 4.6e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.46 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: 0.739 seconds (Warm-up)
#> Chain 3: 1.701 seconds (Sampling)
#> Chain 3: 2.44 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'joint_count' 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: 0.568 seconds (Warm-up)
#> Chain 4: 1.704 seconds (Sampling)
#> Chain 4: 2.272 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] 0.005294961
#>
#> $lower_ci
#> Highest Density Interval: 1.86e-03
#>
#> $upper_ci
#> Highest Density Interval: 9.86e-03
#>
# Calculate mu_critical at habitat size 0.5 z-scores greater than the mean
mu_critical(fit_cov$model, cov_val = c(0,0.5), ci = 0.9)
#> $median
#> [1] 0.004445692
#>
#> $lower_ci
#> Highest Density Interval: 1.51e-03
#>
#> $upper_ci
#> Highest Density Interval: 8.29e-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 0.000527 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 5.27 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: 3.81 seconds (Warm-up)
#> Chain 1: 10.754 seconds (Sampling)
#> Chain 1: 14.564 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 0.000361 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 3.61 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: 4.158 seconds (Warm-up)
#> Chain 2: 9.858 seconds (Sampling)
#> Chain 2: 14.016 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 0.000365 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 3.65 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: 4.064 seconds (Warm-up)
#> Chain 3: 8.212 seconds (Sampling)
#> Chain 3: 12.276 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'joint_count' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 0.000376 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 3.76 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: 4.156 seconds (Warm-up)
#> Chain 4: 10.178 seconds (Sampling)
#> Chain 4: 14.334 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 0.06001695 0.047684312
#> lower_ci 0.01104919 0.008353085
#> upper_ci 0.13716476 0.107476828
# }