sirt: gom.jml – R documentation

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gom.jml

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 λ_{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}, …, g_{pK} )=∑_k λ_{ik} g_{pk} , ∑_k g_{pk}=1

Value

A list with following entries:

`lambda`	Data frame of item parameters λ_{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.

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

Supplementary Item Response Theory Models

v3.10-118

GPL (>= 2)

Authors

Alexander Robitzsch [aut,cre] (<https://orcid.org/0000-0002-8226-3132>)

Initial release

2021-09-22 17:45:34