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Simulate IRW-compliant pairwise-comparison data

Source: R/simulate.R
irw_simdata_comp.Rd

Generates pairwise outcomes among n_agent agents using the Davidson model with ties. (See https://link.springer.com/article/10.3758/s13428-021-01714-2). Returns one row per comparison with agent_a, agent_b, and winner.

Usage

irw_simdata_comp(
  n_agent = 100,
  n_pairs = 10000,
  nu = 0,
  theta = NULL,
  theta_mean = 0,
  theta_sd = 1,
  seed = NULL,
  return_params = FALSE
)

Arguments

n_agent

Integer. Number of agents (ignored if theta provided). Default 100.

n_pairs

Integer. Number of pairwise comparisons to sample. Default 10000.

nu

Numeric. Tie propensity in the Davidson model. Larger values yield more ties. Default 0.

theta

Optional numeric vector of length n_agent with agent abilities. If provided, overrides n_agent. If NULL, sampled from N(0,1).

theta_mean

Mean of the theta distribution (used if theta is NULL). Default 0.

theta_sd

SD of the theta distribution (used if theta is NULL). Default 1.

seed

Optional integer for reproducibility.

return_params

Logical. If TRUE, return a list with data, theta, and nu. Default FALSE.

Value

A data.frame with columns:

  • agent_a (int): index of first agent

  • agent_b (int): index of second agent

  • winner (chr): one of "agent_a","agent_b", or "draw".

If return_params = TRUE, returns a list with:

  • data: the simulated data frame.

  • theta: vector of simulated thetas used

  • nu: tie parameter

Examples

if (FALSE) { # \dontrun{
# --- Basic usage ---
d <- irw_simdata_comp(n_agent = 100, n_pairs = 10000, nu = 0)
head(d)

# Simulate pairwise comparison data and recover abilities with a Davidson model

th <- rnorm(n = 50, mean = 0.5, sd = 3)
pairs <- irw_simdata_comp(
  n_agent = 50, n_pairs = 3000, nu = 0.1,
  theta = th, seed = 1, return_params = TRUE
)

x <- pairs$data
x$winner <- ifelse(x$winner == "agent_b", -1, 1)
x$winner <- ifelse(x$winner == "draw", 0, x$winner)
x$agent_a <- as.factor(x$agent_a)
x$agent_b <- as.factor(x$agent_b)
x$pair <- seq_len(nrow(x))  # add pair id for expandCategorical

library(gnm)
library(BradleyTerry2)

pairs.tri <- expandCategorical(x, "winner", idvar = "pair")

dav <- gnm(
  count ~ GenDavidson(
    winner == 1, winner == 0, winner == -1,
    player1 = agent_a,
    player2 = agent_b
  ) - 1,
  eliminate = pair,
  family = poisson,
  data = pairs.tri
)

plot(
  pairs$theta, coef(dav)[-1],
  xlab = "True theta",
  ylab = "Estimated ability (shifted)",
  main = "Davidson recovery using gnm"
)
abline(lm(coef(dav)[-1] ~ pairs$theta), lty = 2)
} # }