Prepare inputs for hierarchical multinomial probit estimation

Prepares and validates panel (or cross-sectional) choice data for the hierarchical Bayesian multinomial probit with iid \(N(0, \sigma^2)\) utility shocks. The model shares its two-level random-effect structure with prepare_hmnl_data(): respondent-level structural tastes \(\beta_i \sim N(b, W)\) over the covariate_cols (normal only — the probit keeps full conjugacy), and a global alternative-level effect \(\delta_j = z_j'\theta + \xi_j\), \(\xi_j \sim N(0, \sigma_d^2)\).

Usage

prepare_hmnp_data(
  data,
  id_col,
  alt_col,
  choice_col,
  covariate_cols,
  person_col = NULL,
  alt_covariate_cols = NULL,
  outside_opt_label = NULL,
  cf_residual_col = NULL,
  include_outside_option = TRUE
)

Arguments

data: Data frame containing choice data.
id_col: Name of the column identifying choice situations (tasks). Task ids only need to be unique within a respondent.
alt_col: Name of the column identifying alternatives.
choice_col: Name of the column indicating the chosen alternative (1 = chosen, 0 = not chosen).
covariate_cols: Vector of names of structural covariate columns (the random-coefficient dimensions).
person_col: Name of the respondent column grouping choice situations. NULL (default) makes each choice situation its own respondent.
alt_covariate_cols: Names of alternative-level covariate columns (constant within each alternative) forming the \(\delta\) mean function. NULL (default) gives an intercept-only design (P = 1).
outside_opt_label: Label of physical outside-option rows, removed when include_outside_option = TRUE (the outside good is implicit).
cf_residual_col: Name of a first-stage residual column (control function for an endogenous covariate), appended to X. Default NULL.
include_outside_option: Logical; if TRUE (default) an implicit outside option with systematic utility 0 is part of every choice set.

Value

A list of class c("choicer_data_hmnp", "list") with the same components as prepare_hmnl_data() (minus rc_dist).

Details

The returned structure is identical to prepare_hmnl_data() (both preps share one internal engine), except there is no rc_dist field. Unlike prepare_mnp_data(), utilities are NOT differenced against a base alternative: the iid-shock model works in un-differenced utility space, so unbalanced choice sets are supported and the outside option is implicit (its latent utility is a stochastic \(N(0, \sigma^2)\) draw in the kernel, systematic utility 0).

Examples

library(data.table)
set.seed(42)
N <- 20; T <- 3; J <- 4
dt <- data.table(
  pid  = rep(1:N, each = T * J),
  task = rep(seq_len(N * T), each = J),
  alt  = rep(1:J, N * T)
)
dt[, `:=`(x1 = rnorm(.N), x2 = runif(.N, -1, 1))]
#>        pid  task   alt         x1         x2
#>      <int> <int> <int>      <num>      <num>
#>   1:     1     1     1  1.3709584 -0.5341312
#>   2:     1     1     2 -0.5646982  0.1540964
#>   3:     1     1     3  0.3631284  0.6817541
#>   4:     1     1     4  0.6328626 -0.7355924
#>   5:     1     2     1  0.4042683  0.7917824
#>  ---                                        
#> 236:    20    59     4 -0.3909654  0.4483229
#> 237:    20    60     1  1.3487070 -0.2291228
#> 238:    20    60     2 -0.0227647 -0.4036954
#> 239:    20    60     3  0.2442259 -0.8850577
#> 240:    20    60     4 -0.9423717  0.3473859
dt[, choice := 0L]
#>        pid  task   alt         x1         x2 choice
#>      <int> <int> <int>      <num>      <num>  <int>
#>   1:     1     1     1  1.3709584 -0.5341312      0
#>   2:     1     1     2 -0.5646982  0.1540964      0
#>   3:     1     1     3  0.3631284  0.6817541      0
#>   4:     1     1     4  0.6328626 -0.7355924      0
#>   5:     1     2     1  0.4042683  0.7917824      0
#>  ---                                               
#> 236:    20    59     4 -0.3909654  0.4483229      0
#> 237:    20    60     1  1.3487070 -0.2291228      0
#> 238:    20    60     2 -0.0227647 -0.4036954      0
#> 239:    20    60     3  0.2442259 -0.8850577      0
#> 240:    20    60     4 -0.9423717  0.3473859      0
dt[, choice := if (runif(1) < 0.8) sample(c(1L, rep(0L, J - 1))) else 0L,
   by = task]
#>        pid  task   alt         x1         x2 choice
#>      <int> <int> <int>      <num>      <num>  <int>
#>   1:     1     1     1  1.3709584 -0.5341312      0
#>   2:     1     1     2 -0.5646982  0.1540964      0
#>   3:     1     1     3  0.3631284  0.6817541      1
#>   4:     1     1     4  0.6328626 -0.7355924      0
#>   5:     1     2     1  0.4042683  0.7917824      1
#>  ---                                               
#> 236:    20    59     4 -0.3909654  0.4483229      1
#> 237:    20    60     1  1.3487070 -0.2291228      0
#> 238:    20    60     2 -0.0227647 -0.4036954      1
#> 239:    20    60     3  0.2442259 -0.8850577      0
#> 240:    20    60     4 -0.9423717  0.3473859      0
input <- prepare_hmnp_data(dt, "task", "alt", "choice", c("x1", "x2"),
                           person_col = "pid")
input$Ti[1:5]
#> [1] 3 3 3 3 3
input$alt_mapping
#>    alt_int   alt N_OBS N_CHOICES TAKE_RATE MKT_SHARE
#>      <int> <int> <int>     <int>     <num>     <num>
#> 1:       0    NA    60        14 0.2333333 0.2333333
#> 2:       1     1    60        15 0.2500000 0.2500000
#> 3:       2     2    60         8 0.1333333 0.1333333
#> 4:       3     3    60        10 0.1666667 0.1666667
#> 5:       4     4    60        13 0.2166667 0.2166667

Prepare inputs for hierarchical multinomial probit estimation

Usage

Arguments

Value

Details

See also

Examples