The function:

This is a very simple data simulator for the Rasch Model.This is just to get you started, from here is easy to add function parameters for indicating item locations or person distribution characteristics.

1. The function accepts only two parameters:
   • The number of items
   • The number of persons
2. The function creates a list containing three objects:
   • A vector of item locations
   • A vector of person locations
   • A matrix of simulated responses

The code:

rasch.sim         <- function( nitem = 20, npers = 100 ) {

    i.loc         <- rnorm( nitem )
    p.loc         <- rnorm( npers ) 

    temp          <- matrix( rep( p.loc, length( i.loc ) )
                        , ncol = length( i.loc ) )

    logits        <- t( apply( temp, 1, '-', i.loc) )

    probabilities <- 1 / ( 1 + exp( -logits ) )

    resp.prob     <- matrix( probabilities, ncol = nitem)

    obs.resp      <- matrix( sapply( c(resp.prob), rbinom, n = 1, size = 1), ncol = length(i.loc) )

    output        <- list()
    output$i.loc  <- i.loc
    output$p.loc  <- p.loc
    output$resp   <- obs.resp

    output

}

Example:

This is a simple example that uses the Extending the Rasch Model (eRm) package to estimate the model parameters after simulating the data. Do try this at home!

###### Loading Libraries ######

# install.packages('eRm')
library(eRm)

###### Running Simulation ######

sim1              <- rasch.sim( npers = 10000)
sim.parameters    <- sim1$i.loc

###### Estimation Using eRm ######

analysis.eRm      <- RM(sim1$resp)

eRm.estimates     <- (analysis.eRm$betapar) * -1

plot(sim.parameters, eRm.estimates)