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)

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

Value

An object of class prob.guttman
personEstimated person parameters
itemEstimated item parameters
theta.kAbility levels
traitEstimated trait distribution
icInformation criteria
devianceDeviance
iterNumber of iterations
itemdesignSpecified 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

Run this code

##########################################
# 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 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)