# Simple data simulator for the Rasch Model

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### 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.

- The function accepts only two parameters:
- The number of items
- The number of persons

- 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)

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