sirt (version 0.31-20)

modelfit.sirt: Model Fit of Item Response Models

Description

This function calculates a statistic of global model fit while comparing observed and expected item pair correlations.

Usage

modelfit.sirt(object)

Arguments

object

An object generated by rasch.mml2, rasch.mirtlc, rasch.pml2 or

Value

• A list with following entries:
• modelfit
  Model fit statistics: MADcor: mean of absolute deviations in observed and expected correlations (DiBello et al., 2007) MX2: Mean of $\chi^2$ statistics of all item pairs (Chen & Thissen, 1997) MADRESIDCOV: Mean of absolute deviations of residual covariances (McDonald & Mok, 1995) MADQ3: Mean of absolute values of $Q_3$ statistic (Yen, 1984)
• itempairs
  Fit of every item pair

References

Chen, W. & Thissen, D. (1997). Local dependence indexes for item pairs using item response theory. Journal of Educational and Behavioral Statistics, 22, 265-289. DiBello, L. V., Roussos, L. A. and Stout, W. F. (2007) Review of cognitively diagnostic assessment and a summary of psychometric models. In C. R. Rao and S. Sinharay (Eds.), Handbook of Statistics, Vol. 26 (pp. 979--1030). Amsterdam: Elsevier. McDonald, R. P. & Mok, M. M.-C. (1995). Goodness of fit in item response models. Multivariate Behavioral Research, 30, 23-40. Yen, W. M. (1984). Effects of local item dependence on the fit and equating performance of the three-parameter logistic model. Applied Psychological Measurement, 8, 125-145.

Examples

############################################
# Example 1: Reading data
data(data.read)
dat <- data.read
I <- ncol(dat)

# Rasch model
mod1 <- rasch.mml2( dat  )
# Rasch model with smoothed distribution
mod2 <- rasch.mml2( dat , distribution.trait="smooth3" )
# 2PL model
mod3 <- rasch.mml2( dat , distribution.trait="normal" , est.a=1:I )
# 3PL model with equal guessing parameter
mod4 <- rasch.mml2( dat, distribution.trait="smooth3", est.a=1:I, est.c=rep(1,I) )
# Latent class model with 2 classes
mod5 <- rasch.mirtlc( dat , Nclasses=2 )
# Rasch latent class model with 3 classes
mod6 <- rasch.mirtlc( dat , Nclasses=3 , modeltype="MLC1", mmliter=100)

# PML estimation
mod7 <- rasch.pml3( dat )
# Model 8: PML estimation
# Modelling error correlations: 
#          joint residual correlations for each item cluster
error.corr <- diag(1,ncol(dat))
itemcluster <- rep( 1:4 ,each=3 )
for ( ii in 1:3){
    ind.ii <- which( itemcluster == ii )
    error.corr[ ind.ii , ind.ii ] <- ii
        }
mod8 <- rasch.pml3( dat , error.corr = error.corr )

# compare model fit
a1 <- modelfit.sirt(mod1)
a2 <- modelfit.sirt(mod2)
a3 <- modelfit.sirt(mod3)
a4 <- modelfit.sirt(mod4)
a5 <- modelfit.sirt(mod5)
a6 <- modelfit.sirt(mod6)
a7 <- modelfit.sirt(mod7)
a8 <- modelfit.sirt(mod8)