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) -1.95230 0.84509 -2.3102 0.020878 *
#> smoker 2.17646 0.82330 2.6436 0.008203 **
#> gender -0.49579 0.42061 -1.1787 0.238503
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> Count regression coefficients:
#> Estimate StdErr z.value p.value
#> (Intercept) 0.716551 0.179860 3.9839 6.778e-05 ***
#> smoker -0.611777 0.183409 -3.3356 0.0008512 ***
#> gender 0.036389 0.177480 0.2050 0.8375493
#> ---
#> 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) -1.149 0.006 0.31 -1.848 -1.333 -1.119 -0.936 -0.634 2610.283
#> Rhat
#> (Intercept) 1.001
#>
#> Count regression coefficients:
#> mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
#> (Intercept) 0.714 0.003 0.146 0.427 0.615 0.716 0.814 1.000 3029.991
#> smoker -1.066 0.003 0.145 -1.349 -1.163 -1.068 -0.971 -0.780 2303.155
#> gender 0.175 0.003 0.142 -0.100 0.078 0.176 0.272 0.457 2922.114
#> 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: 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 -1032.6 50.5
#> p_loo 189.0 18.5
#> looic 2065.2 101.0
#> ------
#> 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) 419 82.0% 511
#> (0.7, 1] (bad) 70 13.7% <NA>
#> (1, Inf) (very bad) 22 4.3% <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 -994.0 47.2
#> p_waic 150.4 14.0
#> waic 1987.9 94.3
#>
#> 93 (18.2%) p_waic estimates greater than 0.4. We recommend trying loo instead.