Calculates concentration(s) with bootstrap confidence intervals that protect specified proportion(s) of species for individual or model-averaged distributions using parametric or non-parametric bootstrapping.

## Usage

```
ssd_hc(x, ...)
# S3 method for list
ssd_hc(x, percent, proportion = 0.05, ...)
# S3 method for fitdists
ssd_hc(
x,
percent,
proportion = 0.05,
average = TRUE,
ci = FALSE,
level = 0.95,
nboot = 1000,
min_pboot = 0.95,
multi_est = TRUE,
ci_method = "weighted_samples",
parametric = TRUE,
delta = 9.21,
samples = FALSE,
save_to = NULL,
control = NULL,
...
)
# S3 method for fitburrlioz
ssd_hc(
x,
percent,
proportion = 0.05,
ci = FALSE,
level = 0.95,
nboot = 1000,
min_pboot = 0.95,
parametric = FALSE,
samples = FALSE,
save_to = NULL,
...
)
```

## Arguments

- x
The object.

- ...
Unused.

- percent
A numeric vector of percent values to estimate hazard concentrations for. Soft-deprecated for

`proportion = 0.05`

.- proportion
A numeric vector of proportion values to estimate hazard concentrations for.

- average
A flag specifying whether to provide model averaged values as opposed to a value for each distribution.

- ci
A flag specifying whether to estimate confidence intervals (by bootstrapping).

- level
A number between 0 and 1 of the confidence level of the interval.

- nboot
A count of the number of bootstrap samples to use to estimate the confidence limits. A value of 10,000 is recommended for official guidelines.

- min_pboot
A number between 0 and 1 of the minimum proportion of bootstrap samples that must successfully fit (return a likelihood) to report the confidence intervals.

- multi_est
A flag specifying whether to treat the distributions as constituting a single distribution (as opposed to taking the mean) when calculating model averaged estimates.

- ci_method
A string specifying which method to use for estimating the bootstrap values. Possible values are "multi_free" and "multi_fixed" which treat the distributions as constituting a single distribution but differ in whether the model weights are fixed and "weighted_samples" and "weighted_arithmetic" take bootstrap samples from each distribution proportional to its weight versus calculating the weighted arithmetic means of the lower and upper confidence limits.

- parametric
A flag specifying whether to perform parametric bootstrapping as opposed to non-parametrically resampling the original data with replacement.

- delta
A non-negative number specifying the maximum absolute AIC difference cutoff. Distributions with an absolute AIC difference greater than delta are excluded from the calculations.

- samples
A flag specfying whether to include a numeric vector of the bootstrap samples as a list column in the output.

- save_to
NULL or a string specifying a directory to save where the bootstrap datasets and parameter estimates (when successfully converged) to.

- control
A list of control parameters passed to

`stats::optim()`

.

## Details

Model-averaged estimates and/or confidence intervals (including standard error)
can be calculated by treating the distributions as
constituting a single mixture distribution
versus 'taking the mean'.
When calculating the model averaged estimates treating the
distributions as constituting a single mixture distribution
ensures that `ssd_hc()`

is the inverse of `ssd_hp()`

.

If treating the distributions as constituting a single mixture distribution
when calculating model average confidence intervals then
`weighted`

specifies whether to use the original model weights versus
re-estimating for each bootstrap sample unless 'taking the mean' in which case
`weighted`

specifies
whether to take bootstrap samples from each distribution proportional to
its weight (so that they sum to `nboot`

) versus
calculating the weighted arithmetic means of the lower
and upper confidence limits based on `nboot`

samples for each distribution.

Distributions with an absolute AIC difference greater than a delta of by default 7 have considerably less support (weight < 0.01) and are excluded prior to calculation of the hazard concentrations to reduce the run time.

## Methods (by class)

`ssd_hc(list)`

: Hazard Concentrations for Distributional Estimates`ssd_hc(fitdists)`

: Hazard Concentrations for fitdists Object`ssd_hc(fitburrlioz)`

: Hazard Concentrations for fitburrlioz Object

## References

Burnham, K.P., and Anderson, D.R. 2002. Model Selection and Multimodel Inference. Springer New York, New York, NY. doi:10.1007/b97636.

## Examples

```
ssd_hc(ssd_match_moments())
#> # A tibble: 6 × 9
#> dist proportion est se lcl ucl wt nboot pboot
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int> <dbl>
#> 1 gamma 0.05 0.481 NA NA NA 1 0 NA
#> 2 lgumbel 0.05 0.739 NA NA NA 1 0 NA
#> 3 llogis 0.05 0.562 NA NA NA 1 0 NA
#> 4 lnorm 0.05 0.558 NA NA NA 1 0 NA
#> 5 lnorm_lnorm 0.05 0.469 NA NA NA 1 0 NA
#> 6 weibull 0.05 0.501 NA NA NA 1 0 NA
fits <- ssd_fit_dists(ssddata::ccme_boron)
ssd_hc(fits)
#> # A tibble: 1 × 11
#> dist proportion est se lcl ucl wt method nboot pboot samples
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr> <int> <dbl> <I<lis>
#> 1 average 0.05 1.26 NA NA NA 1 parametr… 0 NaN <dbl>
fit <- ssd_fit_burrlioz(ssddata::ccme_boron)
ssd_hc(fit)
#> # A tibble: 1 × 11
#> dist proportion est se lcl ucl wt method nboot pboot samples
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr> <int> <dbl> <I<lis>
#> 1 invpareto 0.05 0.387 NA NA NA 1 non-pa… 0 NA <dbl>
```