Compute aggregate elasticities

Computes a J x J matrix of aggregate elasticities. Entry (i, j) is the percentage change in the probability of choosing alternative i when the attribute of alternative j changes by 1\

Usage

# S3 method for class 'choicer_hb'
elasticities(object, elast_var, eps = 0.01, n_draws = 100L, ...)

elasticities(object, ...)

Arguments

object

A fitted model object.

elast_var

Structural covariate to perturb (hierarchical Bayes methods).

eps

Relative perturbation size (default 0.01).

n_draws

Number of posterior draws to integrate over.

...

Additional arguments passed to methods.

Value

A J x J elasticity matrix with alternative labels.

Methods (by class)

• elasticities(choicer_hb): Posterior-mean aggregate arc elasticities for hierarchical Bayes fits: each inside alternative's elast_var is perturbed by eps (default 1%) and shares are recomputed per posterior draw with a common random-coefficient path, giving \(E_{jk} = (\Delta s_j / s_j) / \epsilon\). Rows are responding alternatives (including the outside option), columns the perturbed alternative.

Examples

# \donttest{
library(data.table)
set.seed(42)
N <- 50; J <- 3
dt <- data.table(id = rep(1:N, each = J), alt = rep(1:J, N))
dt[, `:=`(x1 = rnorm(.N), x2 = rnorm(.N))]
#>         id   alt         x1          x2
#>      <int> <int>      <num>       <num>
#>   1:     1     1  1.3709584 -0.04069848
#>   2:     1     2 -0.5646982 -1.55154482
#>   3:     1     3  0.3631284  1.16716955
#>   4:     2     1  0.6328626 -0.27364570
#>   5:     2     2  0.4042683 -0.46784532
#>  ---                                   
#> 146:    49     2  1.1133860 -0.47733551
#> 147:    49     3 -0.4809928 -0.16626149
#> 148:    50     1 -0.4331690  0.86256338
#> 149:    50     2  0.6968626  0.09734049
#> 150:    50     3 -1.0563684 -1.62561674
dt[, choice := 0L]
#>         id   alt         x1          x2 choice
#>      <int> <int>      <num>       <num>  <int>
#>   1:     1     1  1.3709584 -0.04069848      0
#>   2:     1     2 -0.5646982 -1.55154482      0
#>   3:     1     3  0.3631284  1.16716955      0
#>   4:     2     1  0.6328626 -0.27364570      0
#>   5:     2     2  0.4042683 -0.46784532      0
#>  ---                                          
#> 146:    49     2  1.1133860 -0.47733551      0
#> 147:    49     3 -0.4809928 -0.16626149      0
#> 148:    50     1 -0.4331690  0.86256338      0
#> 149:    50     2  0.6968626  0.09734049      0
#> 150:    50     3 -1.0563684 -1.62561674      0
dt[, choice := sample(c(1L, rep(0L, J - 1))), by = id]
#>         id   alt         x1          x2 choice
#>      <int> <int>      <num>       <num>  <int>
#>   1:     1     1  1.3709584 -0.04069848      0
#>   2:     1     2 -0.5646982 -1.55154482      0
#>   3:     1     3  0.3631284  1.16716955      1
#>   4:     2     1  0.6328626 -0.27364570      0
#>   5:     2     2  0.4042683 -0.46784532      0
#>  ---                                          
#> 146:    49     2  1.1133860 -0.47733551      0
#> 147:    49     3 -0.4809928 -0.16626149      0
#> 148:    50     1 -0.4331690  0.86256338      1
#> 149:    50     2  0.6968626  0.09734049      0
#> 150:    50     3 -1.0563684 -1.62561674      0
fit <- run_mnlogit(dt, "id", "alt", "choice", c("x1", "x2"))
#> Optimization run time 0h:0m:0s
elasticities(fit, "x1")
#>              1             2             3
#> 1  0.002159463 -0.0074958498 -0.0002137027
#> 2 -0.006975639 -0.0008871936 -0.0002137027
#> 3 -0.006975639 -0.0074958498 -0.0068614666
# }