simulateRasch: Simulate raw test scores based on Rasch model

In cNORM: Continuous Norming

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)

cNORM documentation built on Nov. 4, 2024, 5:07 p.m.