sirt (version 0.36-30)

prob.guttman: Probabilistic Guttman Model

Description

This function estimates the probabilistic Guttman model which is a special case of an ordered latent trait model (Hanson 2000, Proctor, 1970).

Usage

prob.guttman(dat, pid = NULL, guess.equal = FALSE,  slip.equal = FALSE, 
    itemlevel = NULL, conv1 = 0.001, glob.conv = 0.001, mmliter = 500)
    
## S3 method for class 'prob.guttman':
summary(object,...)

Arguments

dat

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

pid

Optional vector of person identifiers

guess.equal

Should the same guessing parameters for all the items estimated?

slip.equal

Should the same slipping parameters for all the items estimated?

itemlevel

A vector of item levels of the Guttman scale for each item. If there are $K$ different item levels, then the Guttman scale possesses $K$ ordered trait values.

conv1

Convergence criterion for item parameters

glob.conv

Global convergence criterion for the deviance

mmliter

Maximum number of iterations

object

Object of class prob.guttman

...

Further arguments to be passed

Value

• An object of class prob.guttman
• person
  Estimated person parameters
• item
  Estimated item parameters
• theta.k
  Ability levels
• trait
  Estimated trait distribution
• ic
  Information criteria
• deviance
  Deviance
• iter
  Number of iterations
• itemdesign
  Specified allocation of items to trait levels

References

Hanson, B. (2000). IRT parameter estimation using the EM algorithm. Technical Report. Proctor, C. H. (1970). A probabilistic formulation and statistical analysis for Guttman scaling. Psychometrika, 35, 73-78.

See Also

A summary can be obtained using summary.prob.guttman.

Examples

#############################################################################
# EXAMPLE 1: Dataset Reading
#############################################################################
data(data.read)
dat <- data.read

#***
# Model 1: estimate probabilistic Guttman model
mod1 <- prob.guttman( dat )
summary(mod1)

#***
# Model 2: Guttman model with equal guessing and slipping parameters
mod2 <- prob.guttman( dat , guess.equal=TRUE , slip.equal=TRUE)
summary(mod2)

#***
# Model 3: Guttman model with three a priori specified item levels
itemlevel <- rep(1,12)
itemlevel[ c(2,5,8,10,12) ] <- 2
itemlevel[ c(3,4,6) ] <- 3
mod3 <- prob.guttman( dat , itemlevel=itemlevel )
summary(mod3)