simulateRasch function

Simulate raw test scores based on Rasch model

For testing purposes only: The function simulates raw test scores based on a virtual Rasch based test with n results per age group, an evenly distributed age variable, items.n test items with a simulated difficulty and standard deviation. The development trajectories over age group are modeled by a curve linear function of age, with at first fast progression, which slows down over age, and a slightly increasing standard deviation in order to model a scissor effects. The item difficulties can be accessed via $theta and the raw data via$data of the returned object.

simulateRasch(
  data = NULL,
  n = 100,
  minAge = 1,
  maxAge = 7,
  items.n = 21,
  items.m = 0,
  items.sd = 1,
  Theta = "random",
  width = 1
)

Arguments

• data: data.frame from previous simulations for recomputation (overrides n, minAge, maxAge)
• n: The sample size per age group
• minAge: The minimum age (default 1)
• maxAge: The maximum age (default 7)
• items.n: The number of items of the test
• items.m: The mean difficulty of the items
• items.sd: The standard deviation of the item difficulty
• Theta: irt scales difficulty parameters, either "random" for drawing a random sample, "even" for evenly distributed or a set of predefined values, which then overrides the item.n parameters
• width: The width of the window size for the continuous age per group; +- 1/2 width around group center on items.m and item.sd; if set to FALSE, the distribution is not drawn randomly but normally nonetheless

Returns

a list containing the simulated data and thetas

• data: the data.frame with only age, group and raw
• sim: the complete simulated data with item level results
• theta: the difficulty of the items

Examples

# simulate data for a rather easy test (m = -1.0)
sim <- simulateRasch(n=150, minAge=1,
                     maxAge=7, items.n = 30, items.m = -1.0,
                     items.sd = 1, Theta = "random", width = 1.0)

# Show item difficulties
mean(sim$theta)
sd(sim$theta)
hist(sim$theta)

# Plot raw scores
boxplot(raw~group, data=sim$data)

# Model data
data <- prepareData(sim$data, age="age")
model <- bestModel(data, k = 4)
printSubset(model)
plotSubset(model, type=0)