Simulate paired-comparison data — simulate

Generates dichotomous or ordered paired comparisons from the Bradley–Terry–Luce model. Optional arguments introduce a second object attribute, erratic judges, or within-judge dependence. Generating values are stored in attr(x, "truth").

Usage

simulate_btl(
  n_objects = 8,
  n_judges = 12,
  reps_per_pair = 25,
  model = c("dichotomous", "polytomous", "graded"),
  n_categories = 4,
  object_sd = 1,
  second_attribute = NULL,
  erratic_judges = 0,
  dependence = NULL,
  seed = NULL,
  object_locations = NULL
)

Arguments

n_objects, n_judges: Objects to scale and judges comparing them. Every judge is allocated at least one comparison; the simulator refuses a design with fewer comparisons than judges.
reps_per_pair: Comparisons made of each object pair.
model: "dichotomous" (a winner) or "polytomous" (a rated margin in n_categories categories; an earlier development-era value "graded" is accepted as an alias).
n_categories: Categories for the polytomous model.
object_sd: Realised sample standard deviation of the object locations (evenly spaced and sum-zero).
second_attribute: NULL, or list(rho=): half the judges rank by a second object attribute whose realised correlation with the first is rho. It lies in [-1, 1); at 1 the attributes are identical and no second attribute is planted. This introduces residual dimensionality and possible intransitivity.
erratic_judges: Proportion of judges who choose at random. At least one judge must retain model-based comparisons, in each camp when a second attribute is generated.
dependence: NULL, or list(exposure=, carry_over=): within-judge order effects (a seen-before advantage and a pull from the judge's own earlier verdicts). Adds an order column. Feeds the dependence effects fitted by btl.
seed: Optional non-negative whole-number RNG seed. See rasch_rng for generator support.
object_locations: Optional numeric vector of generated object locations. It must have length n_objects; names, when supplied, must identify the generated objects. Values are centred to identify the origin and take precedence over object_sd.

Value

A data frame of class "rasch_sim": object_a, object_b, winner (or response when polytomous), judge, and order when dependence is planted; with attr(x, "truth").

Examples

d <- simulate_btl(8, 12, erratic_judges = 0.15, seed = 1)
bt <- btl(d, "object_a", "object_b", winner = "winner", judge = "judge")
bt$judges          # the erratic judges carry large fit residuals
#>  judge  n infit_ms outfit_ms fit_resid df_fit
#>     J1 59    0.834     0.724    -1.783 58.410
#>    J10 58    1.362     1.516     2.989 57.420
#>    J11 58    1.021     0.983    -0.117 57.420
#>    J12 58    0.902     0.828    -1.179 57.420
#>     J2 58    0.865     0.836    -1.170 57.420
#>     J3 58    0.958     0.945    -0.369 57.420
#>     J4 59    0.995     0.931    -0.471 58.410
#>     J5 58    1.371     1.528     2.592 57.420
#>     J6 58    1.018     1.057     0.400 57.420
#>     J7 59    0.796     0.876    -0.807 58.410
#>     J8 58    0.812     0.835    -1.226 57.420
#>     J9 59    1.161     1.133     0.724 58.410