sirt (version 0.31-20)

rasch.testlet.glmer: Estimation of the Rasch Testlet Model using Generalized Linear Mixed Effects Models (lme4)

Description

This function is a wrapper to the lme4 generalized linear mixed effects software in Rfor estimating item response models (De Boeck et al., 2011). The estimation of unidimensional models and testlet models of Rasch type (Wang & Wilson, 2005) is implemented.

Usage

rasch.testlet.glmer( dat , testlet.matrix = NULL , 
    link = "logit" , verbose = TRUE , progress=TRUE  )

Arguments

dat

An $N$ times $I$ data frame of dichotomous item responses

testlet.matrix

A vector or a matrix. If it is a vector, the for all the items in dat a testlet identifier should be used. If it is a matrix, then it have two columns where the first columns contains testlet names and the second column contains item names

link

Link function which is used in estimation of the generalized linear mixed effects model (function lmer in Rpackage lme4). The default is the logistic link "logit" which results in the estimation of a Rasch model. Ot

verbose

Print iteration history in lmer?

progress

Print progress?

Value

• A list with the following entries
• mod
  lmer-output of estimated model
• item
  item parameters
• sd.testlet
  standard deviations of trait and testlets
• dat1
  data matrix in long format
• link
  link function
• testlet.matrix
  used design matrix when a testlet model is estimated
• eap
  EAP estimates of person abilities. In testlet models only the EAP estimates of the primary dimension are provided.
• eap.rel
  Reliability of EAP estimates (Adams, 2005)

References

Adams, R. J. (2005). Reliability as a measurement design effect. Studies in Educational Evaluation, 31, 162-172. De Boeck, P., Bakker, M., Zwitser, R., Nivard, M., Hofman, A., Tuerlinckx, F. & Partchev, I. (2011). The estimation of item response models with the lmer function from the lme4 package in R. Journal of Statistical Software, 39(12), 1-28. Goldstein, H. (1980). Dimensionality, bias, independence and measurement scale problems in latent trait test score models. British Journal of Mathematical and Statistical Psychology, 33, 234-246. Wang, W.-C. & Wilson, M. (2005). The Rasch testlet model. Applied Psychological Measurement, 29, 126-149.

See Also

For estimating marginal item response models which account for deviations of local independence see rasch.copula2, rasch.pml3 or rasch.pairwise.itemcluster.

Examples

# load reading example data set
data(data.read)

# define testlet matrix
testlet.matrix <- data.frame( substring( colnames(data.read),1,1) , colnames(data.read))

# Rasch model
mod <- rasch.testlet.glmer(data.read )

# linear probability model
mod <- rasch.testlet.glmer(data.read , link = "linear")

# cloglog link function
mod <- rasch.testlet.glmer(data.read , link = "cloglog")

# Rasch testlet model
mod <- rasch.testlet.glmer(data.read , testlet.matrix = testlet.matrix )
##   [...]
##   Standard deviations
##       effect    SD
##   1    trait 1.060
##   2        A 0.682
##   3        B 0.000
##   4        C 1.570
##   5 Residual 1.814
##   
##   EAP reliability: 0.534 

# Rasch testlet models (with two testlets and 
#   some items without any testlet structure)
mod <- rasch.testlet.glmer(data.read , 
    testlet.matrix = testlet.matrix[ c(1:4 , 9:12) , ] )

# linear probability model with testlet structure
mod <- rasch.testlet.glmer(data.read , testlet.matrix = testlet.matrix , link="linear")

# loglog link function with testlet structure
mod <- rasch.testlet.glmer(data.read , testlet.matrix = testlet.matrix , link="loglog")