Simulate Data from a Rasch Model

Creates fake response data where you KNOW the true parameters. This is useful for testing that the model works (parameter recovery), learning the package, and running simulation studies.

Usage

rasch_simulate(
  J = 200,
  K = 10,
  delta_true = 0.75,
  alpha_sd = 1,
  beta = NULL,
  seed = NULL
)

Arguments

J

Number of students. Default 200.

K

Number of questions. Default 10.

delta_true

True mean ability. Default 0.75 (matches the prior).

alpha_sd

Standard deviation of student ability deviations. Default 1.

beta

Values for item difficulties. If NULL, creates K evenly spaced values from -2 (easiest) to 2 (hardest).

seed

Random seed for reproducibility. Same seed = same data every time.

Value

A list with:

data

A J x K matrix of 0/1 responses.

delta

The true mean ability used.

alpha

Vector of true student deviations (length J).

beta

Vector of true item difficulties (length K).

Examples

sim <- rasch_simulate(J = 100, K = 5, seed = 42)
head(sim$data) # first few rows of the response matrix
#>    Q1 Q2 Q3 Q4 Q5
#> S1  1  1  1  1  1
#> S2  1  1  1  0  0
#> S3  1  1  1  1  1
#> S4  1  1  1  0  0
#> S5  1  1  0  1  0
#> S6  1  0  1  1  0
sim$beta # true item difficulties
#> [1] -2 -1  0  1  2
sim$delta # true mean ability
#> [1] 0.75