Bell regression model — bellreg • bellreg

Fits the Bell regression model to overdispersed count data.

Usage

bellreg(
  formula,
  data = NULL,
  approach = c("mle", "bayes"),
  link = c("log", "sqrt", "identity"),
  priors = prior_spec(list(intercept ~ normal(0, 10), beta ~ normal(0, 2.5)), autoscale =
    TRUE),
  ...
)

Arguments

formula: an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.
data: an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which ypbp is called.
approach: approach to be used to fit the model (mle: maximum likelihood; bayes: Bayesian approach).
link: assumed link function (log, sqrt or identiy); default is log.
priors: a list containing the prior specification for the parameters; if NULL, default prior are used.
...: further arguments passed to either rstan::optimizing or rstan::sampling.

Value

bellreg returns an object of class "bellreg" containing the fitted model.

Examples

# \donttest{
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) 0.98524220 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 =   AIC = 181.9228 

# Bayesian approach:
bayes <- bellreg(nf ~ lroll, data = faults, approach = "bayes", refresh = FALSE)
summary(bayes)
#> Call:
#> bellreg(formula = nf ~ lroll, data = faults, approach = "bayes", 
#>     refresh = FALSE)
#> 
#> Prior specifications: 
#> intercept ~ normal(0, 10)
#> beta ~ normal(0, 2.5)
#> 
#> Summary of the posterior distribution: 
#>               mean     sd   2.5%    50%  97.5%    n_eff   Rhat
#> (Intercept) 0.9823 0.3229 0.3348 0.9832 1.6020 2585.683 0.9996
#> lroll       0.0019 0.0005 0.0010 0.0019 0.0028 2957.287 0.9996
#> 
#> 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.
#> 
# }