Simulating Ordinal Data

[Ilker Soyturk]

Can anyone provide syntax for data simulation for ordinal (likert-scale) data? I have standardized path coefficient for a model and I want to generate a simulated data for educational purposes. I do not know if it has been answered anywhere but any help will be appreciated

Thanks!. 

[Nickname]

Ilker,
  Here is a simple CFA example.

# Simulate ordinal data

require(lavaan)

# see ?model.syntax for details
simModel <- '
  factor =~ .8*item1 + .8*item2 + .8*item3 + .8*item4 # factor loadings
  item1 | -1*t1 + -.5*t2 + 0*t3 + .5*t4 + 1*t5 # thresholds
  item2 | -1*t1 + -.5*t2 + 0*t3 + .5*t4 + 1*t5
  item3 | -1*t1 + -.5*t2 + 0*t3 + .5*t4 + 1*t5
  item4 | -1*t1 + -.5*t2 + 0*t3 + .5*t4 + 1*t5
  factor ~ 0*1 # zero intercepts (not required)
  item1 ~ 0*1
  item2 ~ 0*1
  item3 ~ 0*1
  item4 ~ 0*1
  factor ~~ 1*factor # variances
  item1 ~~ 1*item1
  item2 ~~ 1*item2
  item3 ~~ 1*item3
  item4 ~~ 1*item4
' # end simModel


lavaanify(simModel)
ordinalData <- simulateData(simModel, sample.nobs=1000)
head(ordinalData, 10)
summary(ordinalData)

fitModel <- '
  factor =~ item1 + item2 + item3 + item4
  item1 | t1 + t2 + t3 + t4 + t5
  item2 | t1 + t2 + t3 + t4 + t5
  item3 | t1 + t2 + t3 + t4 + t5
  item4 | t1 + t2 + t3 + t4 + t5
  factor ~~ 1*factor
  item1 ~~ item1
  item2 ~~ item2
  item3 ~~ item3
  item4 ~~ item4
' # end fitModel
 
lavaanify(fitModel)
ordinalFit <- lavaan(model=fitModel, data=ordinalData)
summary(ordinalFit) # note unique variances rescaled

Keith
------------------------
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/