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) -1.95125 0.84424 -2.3113 0.020819 *
#> smoker 2.17553 0.82248 2.6451 0.008167 **
#> gender -0.49601 0.42059 -1.1793 0.238275
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> Count regression coefficients:
#> Estimate StdErr z.value p.value
#> (Intercept) 0.716784 0.179844 3.9856 6.731e-05 ***
#> smoker -0.611842 0.183398 -3.3361 0.0008495 ***
#> gender 0.036218 0.177484 0.2041 0.8383045
#> ---
#> 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 -1.932 -1.343 -1.119 -0.93 -0.622 1966.336
#> Rhat
#> (Intercept) 1
#>
#> Count regression coefficients:
#> mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
#> (Intercept) 0.714 0.003 0.145 0.425 0.616 0.716 0.812 1.000 2965.117
#> smoker -1.070 0.003 0.145 -1.354 -1.164 -1.071 -0.972 -0.789 2519.677
#> gender 0.176 0.002 0.135 -0.092 0.086 0.177 0.267 0.443 3091.451
#> Rhat
#> (Intercept) 1
#> smoker 1
#> gender 1
#> ---
#> 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: Some Pareto k diagnostic values are too high. See help('pareto-k-diagnostic') for details.
#>
#> Computed from 4000 by 511 log-likelihood matrix.
#>
#> Estimate SE
#> elpd_loo -1036.1 50.8
#> p_loo 191.8 18.1
#> looic 2072.3 101.6
#> ------
#> MCSE of elpd_loo is NA.
#> MCSE and ESS estimates assume independent draws (r_eff=1).
#>
#> Pareto k diagnostic values:
#> Count Pct. Min. ESS
#> (-Inf, 0.7] (good) 418 81.8% 2769
#> (0.7, 1] (bad) 75 14.7% <NA>
#> (1, Inf) (very bad) 18 3.5% <NA>
#> See help('pareto-k-diagnostic') for details.
loo::waic(log_lik)
#> Warning:
#> 93 (18.2%) p_waic estimates greater than 0.4. We recommend trying loo instead.
#>
#> Computed from 4000 by 511 log-likelihood matrix.
#>
#> Estimate SE
#> elpd_waic -998.0 47.5
#> p_waic 153.7 14.2
#> waic 1996.1 95.1
#>
#> 93 (18.2%) p_waic estimates greater than 0.4. We recommend trying loo instead.