Estimate a Random Effects Negative Binomial regression model

Usage

renb(
  formula,
  group_var,
  data,
  method = "NM",
  max.iters = 1000,
  print.level = 0,
  bootstraps = NULL,
  offset = NULL
)

Arguments

formula: an R formula.
group_var: the grouping variable(s) for the random effects (e.g., individual ID or other panel ID variables).
data: a dataframe that has all of the variables in the formula.
method: a method to use for optimization in the maximum likelihood estimation. For options, see maxLik. Note that "BHHH" is not available for this function due to the implementation for the random effects.
max.iters: the maximum number of iterations to allow the optimization method to perform.
print.level: Integer specifying the verbosity of output during optimization.
bootstraps: Optional integer specifying the number of bootstrap samples to be used for estimating standard errors. If not specified, no bootstrapping is performed.
offset: an optional offset term provided as a string.

Value

An object of class `countreg` which is a list with the following components:

model: the fitted model object.
data: the data frame used to fit the model.
call: the matched call.
formula: the formula used to fit the model.

Details

This function estimates a random effects negative binomial (RENB) regression model. This model is based on the NB-1 model. The PDF for the RENB is: $$f(y_{it}|\mu_{it}, a, b) = \frac{\Gamma(a+b) + \Gamma(a + \sum_{t = 1}^{n_i} \mu_{it}) + \Gamma(b + \sum_{t=1}^{n_i}y_{it})} {\Gamma(a) \Gamma(b) \Gamma(a + b + \sum_{t=1}^{n_i}\mu_{it} + \sum_{t=1}^{n_i}y_{it})} \prod_{t=1}^{n_i} \frac{\Gamma(\mu_{it}+y_{it})}{\Gamma(\mu_{it})\Gamma(y_{it})}$$

Examples

# \donttest{
## RENB Model
data("washington_roads")
washington_roads$AADTover10k <- 
  ifelse(washington_roads$AADT > 10000, 1, 0) # create a dummy variable
renb.mod <- renb(Animal ~ lnaadt + speed50 + ShouldWidth04 + AADTover10k,
                                data=washington_roads,
                                offset = "lnlength",
                                group_var="ID",
                                method="nm",
                                max.iters = 1000)
summary(renb.mod)
#> Call:
#>  Animal ~ lnaadt + speed50 + ShouldWidth04 + AADTover10k 
#> 
#>  Method:  RENB 
#> Iterations:  746 
#> Convergence:  successful convergence  
#> Log-likelihood:  -263.7988 
#> 
#> Parameter Estimates:
#> # A tibble: 8 × 7
#>   parameter           coeff `Std. Err.` `t-stat` `p-value` `lower CI` `upper CI`
#>   <chr>               <dbl>       <dbl>    <dbl>     <dbl>      <dbl>      <dbl>
#> 1 (Intercept)        -7.05        0.127   -55.7      0         -7.30      -6.80 
#> 2 lnaadt              0.972       0.015    64.6      0          0.942      1.00 
#> 3 speed50            -0.985       0.301    -3.27     0.001     -1.58      -0.395
#> 4 ShouldWidth04      -0.414       0.212    -1.96     0.051     -0.828      0.001
#> 5 AADTover10k        -0.861       0.447    -1.92     0.054     -1.74       0.015
#> 6 ln(a)               3.01        0.115    26.2      0          2.78       3.23 
#> 7 ln(b)               0.604       0.122     4.97     0          0.366      0.843
#> 8 lnlength (Offset …  1          NA        NA       NA         NA         NA    
# }