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Modeling count data with the Bell distribution

library(bellreg)

data(faults)

# ML approach:
mle <- bellreg(nf ~ lroll, data = faults, approach = "mle")
summary(mle)
#> Call:
#> bellreg(formula = nf ~ lroll, data = faults, approach = "mle")
#> 
#> Coefficients:
#>               Estimate     StdErr z.value   p.value    
#> (Intercept) 0.98524443 0.33219412  2.9659  0.003018 ** 
#> lroll       0.00190935 0.00049003  3.8964 9.765e-05 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> logLik = -88.96139   AIC = 181.9228

# Bayesian approach:
bayes <- bellreg(nf ~ lroll, data = faults, approach = "bayes", refresh = FALSE)
summary(bayes)
#> 
#> bellreg(formula = nf ~ lroll, data = faults, approach = "bayes", 
#>     refresh = FALSE)
#> 
#>              mean se_mean    sd  2.5%   25%   50%   75% 97.5%    n_eff  Rhat
#> (Intercept) 0.991   0.007 0.331 0.329 0.767 1.000 1.212 1.625 2103.403 1.000
#> lroll       0.002   0.000 0.000 0.001 0.002 0.002 0.002 0.003 2394.623 0.999
#> 
#> Inference for Stan model: bellreg.
#> 4 chains, each with iter=2000; warmup=1000; thin=1; 
#> post-warmup draws per chain=1000, total post-warmup draws=4000.

log_lik <- loo::extract_log_lik(bayes$fit)
loo::loo(log_lik)
#> 
#> Computed from 4000 by 32 log-likelihood matrix.
#> 
#>          Estimate  SE
#> elpd_loo    -91.0 3.9
#> p_loo         2.0 0.6
#> looic       182.1 7.9
#> ------
#> MCSE of elpd_loo is 0.0.
#> MCSE and ESS estimates assume independent draws (r_eff=1).
#> 
#> All Pareto k estimates are good (k < 0.7).
#> See help('pareto-k-diagnostic') for details.
loo::waic(log_lik)
#> Warning: 
#> 1 (3.1%) p_waic estimates greater than 0.4. We recommend trying loo instead.
#> 
#> Computed from 4000 by 32 log-likelihood matrix.
#> 
#>           Estimate  SE
#> elpd_waic    -91.0 3.9
#> p_waic         1.9 0.6
#> waic         182.0 7.9
#> 
#> 1 (3.1%) p_waic estimates greater than 0.4. We recommend trying loo instead.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.