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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,...)

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.

Examples