Calculates the logarithmic, quadratic/Brier and spherical score from a model with binary or count outcome.

## Details

Proper scoring rules can be used to evaluate the quality of model
predictions and model fit. `performance_score()`

calculates the logarithmic,
quadratic/Brier and spherical scoring rules. The spherical rule takes values
in the interval `[0, 1]`

, with values closer to 1 indicating a more
accurate model, and the logarithmic rule in the interval `[-Inf, 0]`

,
with values closer to 0 indicating a more accurate model.

For `stan_lmer()`

and `stan_glmer()`

models, the predicted values
are based on `posterior_predict()`

, instead of `predict()`

. Thus,
results may differ more than expected from their non-Bayesian counterparts
in **lme4**.

## Note

Code is partially based on GLMMadaptive::scoring_rules().

## References

Carvalho, A. (2016). An overview of applications of proper scoring rules. Decision Analysis 13, 223–242. doi:10.1287/deca.2016.0337

## Examples

```
## Dobson (1990) Page 93: Randomized Controlled Trial :
counts <- c(18, 17, 15, 20, 10, 20, 25, 13, 12)
outcome <- gl(3, 1, 9)
treatment <- gl(3, 3)
model <- glm(counts ~ outcome + treatment, family = poisson())
performance_score(model)
#> # Proper Scoring Rules
#>
#> logarithmic: -2.5979
#> quadratic: 0.2095
#> spherical: 0.3238
# \donttest{
data(Salamanders, package = "glmmTMB")
model <- glmmTMB::glmmTMB(
count ~ spp + mined + (1 | site),
zi = ~ spp + mined,
family = nbinom2(),
data = Salamanders
)
performance_score(model)
#> # Proper Scoring Rules
#>
#> logarithmic: -1.3275
#> quadratic: 262.1651
#> spherical: 0.0316
# }
```