simulateRasch {cNORM}

Simulate raw test scores based on Rasch model

Description

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.

Usage

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

Value

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)