Zero-inflated Bell model

library(bellreg)

data(cells)

# ML approach:
mle <- zibellreg(cells ~ smoker+gender|smoker+gender, data = cells, approach = "mle")
summary(mle)
#> Call:
#> zibellreg(formula = cells ~ smoker + gender | smoker + gender, 
#>     data = cells, approach = "mle")
#> 
#> Zero-inflated regression coefficients:
#>             Estimate   StdErr z.value  p.value   
#> (Intercept) -1.95188  0.84474 -2.3106 0.020854 * 
#> smoker       2.17611  0.82296  2.6442 0.008188 **
#> gender      -0.49585  0.42060 -1.1789 0.238431   
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> 
#> Count regression coefficients:
#>              Estimate    StdErr z.value   p.value    
#> (Intercept)  0.716720  0.179855  3.9850 6.748e-05 ***
#> smoker      -0.611764  0.183405 -3.3356 0.0008512 ***
#> gender       0.036213  0.177482  0.2040 0.8383240    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> --- 
#> logLik = -610.3234   AIC = 1232.647

# Bayesian approach:
bayes <- zibellreg(cells ~ 1|smoker+gender, data = cells, approach = "bayes", refresh = FALSE)
summary(bayes)
#> Call:
#> zibellreg(formula = cells ~ 1 | smoker + gender, data = cells, 
#>     approach = "bayes", refresh = FALSE)
#> 
#> Zero-inflated regression coefficients:
#>               mean se_mean    sd   2.5%    25%    50%    75%  97.5%    n_eff
#> (Intercept) -1.163   0.008 0.341 -1.961 -1.338 -1.121 -0.936 -0.619 1624.737
#>              Rhat
#> (Intercept) 1.002
#> 
#> Count regression coefficients:
#>               mean se_mean    sd   2.5%    25%    50%    75%  97.5%    n_eff
#> (Intercept)  0.720   0.003 0.145  0.441  0.622  0.719  0.818  1.005 2909.966
#> smoker      -1.075   0.003 0.145 -1.361 -1.173 -1.075 -0.979 -0.787 2404.475
#> gender       0.170   0.003 0.139 -0.107  0.080  0.169  0.263  0.448 2792.616
#>              Rhat
#> (Intercept) 1.000
#> smoker      1.001
#> gender      1.000
#> --- 
#> Inference for Stan model: zibellreg.
#> 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)
#> Warning: Relative effective sample sizes ('r_eff' argument) not specified.
#> For models fit with MCMC, the reported PSIS effective sample sizes and 
#> MCSE estimates will be over-optimistic.
#> 
#> Computed from 4000 by 511 log-likelihood matrix
#> 
#>          Estimate   SE
#> elpd_loo   -626.8 24.8
#> p_loo         4.5  0.4
#> looic      1253.5 49.5
#> ------
#> Monte Carlo SE of elpd_loo is 0.0.
#> 
#> All Pareto k estimates are good (k < 0.5).
#> See help('pareto-k-diagnostic') for details.
loo::waic(log_lik)
#> 
#> Computed from 4000 by 511 log-likelihood matrix
#> 
#>           Estimate   SE
#> elpd_waic   -626.8 24.8
#> p_waic         4.5  0.4
#> waic        1253.5 49.5