The goal of bellreg is to provide a set of functions to fit regression models for count data with overdispersion using the Bell distribution. The implemented models account for ordinary and zero-inflated regression models under both frequentist and Bayesian approaches. Theoretical details regarding the models implemented in the package can be found in Castellares et al. (2018) doi:10.1016/j.apm.2017.12.014 and Lemonte et al. (2020) doi:10.1080/02664763.2019.1636940.
Installation
You can install the development version of bellreg from GitHub with:
# install.packages("devtools")
devtools::install_github("fndemarqui/bellreg")Example
library(bellreg)
data(faults)
# ML approach:
mle <- bellreg(nf ~ lroll, data = faults, approach = "mle", init = 0)
summary(mle)
#> Call:
#> bellreg(formula = nf ~ lroll, data = faults, approach = "mle",
#> init = 0)
#>
#> Coefficients:
#> Estimate StdErr z.value p.value
#> (Intercept) 0.98524220 0.33219474 2.9659 0.003018 **
#> lroll 0.00190934 0.00049004 3.8963 9.766e-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) 0.984 0.007 0.334 0.331 0.758 0.978 1.213 1.627 2222.313 1.001
#> lroll 0.002 0.000 0.000 0.001 0.002 0.002 0.002 0.003 2478.992 1.001
#>
#> 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.