Marginal Effects, Elasticities, and Pseudo-Elasticities for flexCountReg Models

Compute average marginal effects (AMEs), elasticities, or pseudo-elasticities for fitted flexCountReg objects. Standard errors are computed using either the delta method or a bootstrap, and the results can be returned as a tibble, a gt table, or a LaTeX table.

Usage

margEffTable(
  object,
  data = NULL,
  vars = NULL,
  measure = c("auto", "ame", "elasticity"),
  indicator = c("pseudo_elasticity", "discrete_change"),
  se = c("delta", "bootstrap"),
  bootstraps = 200,
  pred_method = NULL,
  confint_level = 0.95,
  tableType = c("tibble", "gt", "latex"),
  digits = 3,
  cluster_var = NULL,
  ...
)

Arguments

object

A fitted flexCountReg object.

data

Optional data frame. Defaults to the data used to fit the model.

vars

Optional character vector of variable names to evaluate. If NULL, the function uses the non-response variables appearing in the model formula that are present in data.

measure

Character scalar. One of:

"auto"

Continuous variables receive AMEs; indicator variables receive pseudo-elasticities (or discrete changes if indicator = "discrete_change").

"ame"

Compute average marginal effects for continuous variables.

"elasticity"

Compute elasticities for continuous variables. Indicator variables receive pseudo-elasticities (or discrete changes if indicator = "discrete_change").

indicator

Character scalar. For indicator variables, return "pseudo_elasticity" (default) or "discrete_change".

se

Character scalar. Standard error method: "delta" (default) or "bootstrap".

bootstraps

Integer. Number of bootstrap replications when se = "bootstrap".

pred_method

Optional prediction method forwarded to predict.flexCountReg(). For random-parameters models, this is commonly "Exact" or "Simulated". If NULL, the function uses "Exact" for random-parameters models when possible.

confint_level

Numeric scalar between 0 and 1. Confidence level for the confidence interval. Default is 0.95.

tableType

Character scalar. One of "tibble", "gt", or "latex".

digits

Integer. Number of digits to round in the returned table.

cluster_var

Optional character vector giving a clustering variable for bootstrap resampling. If supplied, bootstrap samples are drawn at the cluster level. If omitted, the function attempts row-level bootstrap resampling.

...

Additional arguments passed to predict.flexCountReg().

Value

A table object of the type requested by tableType. For "tibble", the returned object also carries an effect_info attribute with metadata about the calculation.

Details

Continuous variables are handled by numerical differentiation on the expected-response scale. Indicator variables are handled by discrete changes (or pseudo-elasticities, depending on indicator).

The function works on the expected-response scale and is intended to be compatible with all fitted flexCountReg model types, provided that predict.flexCountReg() can generate predictions for the model.

For continuous regressors, the average marginal effect is computed using a central finite difference: $$ \text{AME}_j = \frac{1}{n}\sum_{i=1}^n \frac{\mu_i(x_{ij}+h)-\mu_i(x_{ij}-h)}{2h} $$ where \(\mu_i\) is the predicted mean response.

For elasticities, the effect is computed as: $$ E_j = \frac{1}{n}\sum_{i=1}^n \left(\frac{x_{ij}}{\mu_i}\frac{\partial \mu_i}{\partial x_{ij}}\right) $$

For indicator variables, the function computes a discrete change between the observed baseline and a switched value. If indicator = "pseudo_elasticity", the result is reported as a percent change relative to the baseline.

Examples

# \donttest{
data("washington_roads")
washington_roads$AADT10kplus <- ifelse(washington_roads$AADT > 10000, 1, 0)

nb2 <- countreg(
  Total_crashes ~ lnaadt + lnlength + speed50 + AADT10kplus,
  data = washington_roads,
  family = "NB2"
)

margEffTable(nb2, tableType = "tibble")
#> Marginal Effects / Elasticities
#> Method: delta 
#> 
#>         term variable_type           effect_metric estimate std_error t_value
#>       lnaadt    continuous Average marginal effect    0.423     0.033  12.710
#>     lnlength    continuous Average marginal effect    0.394     0.038  10.241
#>      speed50     indicator   Pseudo-elasticity (%)  -36.701     6.759  -5.430
#>  AADT10kplus     indicator   Pseudo-elasticity (%)  124.032    29.366   4.224
#>  p_value sig lower_ci upper_ci n_obs successful_bootstraps
#>        0 ***    0.358    0.489  1501                    NA
#>        0 ***    0.318    0.469  1501                    NA
#>        0 ***  -49.950  -23.453  1501                    NA
#>        0 ***   66.475  181.588  1501                    NA
margEffTable(nb2, tableType = "gt")


  
Marginal Effects / Elasticities
    
Method: delta
    
term
      
variable_type
      
effect_metric
      
estimate
      
std_error
      
t_value
      
p_value
      
sig
      
lower_ci
      
upper_ci
      
n_obs
      
successful_bootstraps
    
lnaadt
continuous
Average marginal effect
0.423
0.033
12.710
0.000
***
0.358
0.489
1501
NA
lnlength
continuous
Average marginal effect
0.394
0.038
10.241
0.000
***
0.318
0.469
1501
NA
speed50
indicator
Pseudo-elasticity (%)
−36.701
6.759
−5.430
0.000
***
−49.950
−23.453
1501
NA
AADT10kplus
indicator
Pseudo-elasticity (%)
124.032
29.366
4.224
0.000
***
66.475
181.588
1501
NA
Significance codes: * p <= 0.05, ** p <= 0.01, *** p <= 0.001.
    
# }