gom.jml: Grade of Membership Model (Joint Maximum Likelihood...

In sirt: Supplementary Item Response Theory Models

Grade of Membership Model (Joint Maximum Likelihood Estimation)

Description

This function estimates the grade of membership model employing a joint maximum likelihood estimation method (Erosheva, 2002; p. 23ff.).

Usage

gom.jml(dat, K=2, seed=NULL, globconv=0.001, maxdevchange=0.001,
        maxiter=600, min.lambda=0.001, min.g=0.001)

Arguments

dat	Data frame of dichotomous item responses
K	Number of classes
seed	Seed value of random number generator. Deterministic starting values are used for the default value NULL.
globconv	Global parameter convergence criterion
maxdevchange	Maximum change in relative deviance
maxiter	Maximum number of iterations
min.lambda	Minimum \lambda_{ik} parameter to be estimated
min.g	Minimum g_{pk} parameter to be estimated

Details

The item response model of the grade of membership model with K classes for dichotomous correct responses X_{pi} of person p on item i is

P(X_{pi}=1 | g_{p1}, \ldots, g_{pK} )=\sum_k \lambda_{ik} g_{pk} \quad, \quad \sum_k g_{pk}=1

Value

A list with following entries:

lambda	Data frame of item parameters \lambda_{ik}
g	Data frame of individual membership scores g_{pk}
g.mean	Mean membership scores
gcut	Discretized membership scores
gcut.distr	Distribution of discretized membership scores
K	Number of classes
deviance	Deviance
ic	Information criteria
N	Number of students
score	Person score
iter	Number of iterations
datproc	List with processed data (recoded data, starting values, ...)
...	Further values

References

Erosheva, E. A. (2002). Grade of membership and latent structure models with application to disability survey data. PhD thesis, Carnegie Mellon University, Department of Statistics.

See Also

S3 method summary.gom

Examples

#############################################################################
# EXAMPLE 1: TIMSS data
#############################################################################

data( data.timss)
dat <- data.timss$data[, grep("M", colnames(data.timss$data) ) ]

# 2 Classes (deterministic starting values)
m2 <- sirt::gom.jml(dat,K=2, maxiter=10 )
summary(m2)

## Not run: 
# 3 Classes with fixed seed and maximum number of iterations
m3 <- sirt::gom.jml(dat,K=3, maxiter=50,seed=89)
summary(m3)

## End(Not run)

sirt documentation built on May 29, 2024, 8:43 a.m.