Simple data simulator for the 2PL model

[This article was first published on R Snippets for IRT, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

The function:

This is a very simple data simulator for a 2PL Model. This is just to get you started, from here is easy to add function parameters for indicating item locations and slopes 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 four objects:
    • A vector of item locations
    • A vector of item slopes
    • A vector of person locations
    • A matrix of simulated responses

The code:

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

i.loc         <- rnorm( nitem )
p.loc         <- rnorm( npers )
i.slp         <- rlnorm( nitem, sdlog = .4 )

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

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

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$i.loc  <- i.loc
output$i.slp  <- i.slp
output$p.loc  <- p.loc
output$resp   <- obs.resp



This is a simple example that uses the IRToys (irtoys) package to estimate the model parameters after simulating the data. Do try this at home too!


# Note: 'irtoys' might not load right away in OSX. You can try the following sequence in that case:
# install.packages('mvtnorm')
# install.packages('msm')
# install.packages('ltm',type='source')
# install.packages('irtoys',type='source')


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

data2pl <- twopl.sim(nitem=20,npers=10000)

sim.loc.param <- data2pl$i.loc
sim.slp.param <- data2pl$i.slp

###### Estimation Using irtoys ######

analysis.2pl  <- est(data2pl$resp, model = '2PL', engine = 'ltm')

est.slp.param <- analysis.2pl[,1]
est.loc.param <- analysis.2pl[,2]



To leave a comment for the author, please follow the link and comment on their blog: R Snippets for IRT. offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)