Finds the ASC (delta) parameters such that predicted market shares match target shares, using the contraction mapping of Berry, Levinsohn, and Pakes (1995) doi:10.2307/2171802 .
Examples
# \donttest{
library(data.table)
#>
#> Attaching package: ‘data.table’
#> The following object is masked from ‘package:base’:
#>
#> %notin%
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
blp(fit, target_shares = rep(1/J, J))
#> [,1]
#> [1,] 0.00000000
#> [2,] -0.03013133
#> [3,] 0.01204404
# }