Prepare inputs for Bayesian multinomial probit estimation

Prepares and validates inputs for Bayesian multinomial probit estimation. Covariates are differenced against the base alternative, so the design matrix has one row per (choice situation, non-base alternative) pair. Balanced choice sets are required: every choice situation must contain the same \(J\) alternatives.

Usage

prepare_mnp_data(
  data,
  id_col,
  alt_col,
  choice_col,
  covariate_cols,
  base_alt = NULL,
  use_asc = TRUE
)

Arguments

data

Data frame containing choice data.

id_col

Name of the column identifying choice situations (individuals).

alt_col

Name of the column identifying alternatives.

choice_col

Name of the column indicating chosen alternative (1 = chosen, 0 = not chosen).

covariate_cols

Vector of names of columns to be used as covariates.

base_alt

Label of the base (reference) alternative used for utility differencing. If NULL (default), the first alternative in sort order is used.

use_asc

Logical indicating whether to include alternative-specific constants (one intercept per non-base alternative).

Value

A list containing:

• X: Stacked differenced design matrix ((N * p) x K), covariate columns first, then ASC columns when use_asc = TRUE.

• y: Integer vector of choices (0 = base alternative, j in 1..p for the j-th non-base alternative), one per choice situation.

• p: Number of utility differences (J - 1).

• J: Number of alternatives.

• N: Number of choice situations.

• K: Number of columns of X.

• alt_mapping: Data.table mapping alternatives to summary statistics (the base alternative is alt_int = 1).

• base_alt: Resolved label of the base alternative.

• param_map: Named list of integer index vectors (beta, asc).

• use_asc: Logical flag.

• dropped_cols: Names of columns dropped due to collinearity, if any.

• data_spec: List with column name metadata.

Examples

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
input <- prepare_mnp_data(dt, "id", "alt", "choice", c("x1", "x2"))
str(input$X)
#>  num [1:100, 1:4] -1.936 -1.008 -0.229 -0.739 -1.606 ...
#>  - attr(*, "dimnames")=List of 2
#>   ..$ : NULL
#>   ..$ : chr [1:4] "x1" "x2" "ASC_2" "ASC_3"
input$alt_mapping
#> Key: <alt_int, alt>
#>    alt_int   alt N_OBS N_CHOICES TAKE_RATE MKT_SHARE
#>      <int> <int> <int>     <int>     <num>     <num>
#> 1:       1     1    50        17      0.34      0.34
#> 2:       2     2    50        21      0.42      0.42
#> 3:       3     3    50        12      0.24      0.24