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 prob.guttman
summary(object,...)
# S3 method for prob.guttman
anova(object,...)
# S3 method for prob.guttman
logLik(object,...)
# S3 method for prob.guttman
IRT.irfprob(object,...)
# S3 method for prob.guttman
IRT.likelihood(object,...)
# S3 method for prob.guttman
IRT.posterior(object,...)

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

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

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.