Grade of Membership Model (Joint Maximum Likelihood Estimation)

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.

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)

if (FALSE) {
# 3 Classes with fixed seed and maximum number of iterations
m3 <- sirt::gom.jml(dat,K=3, maxiter=50,seed=89)
summary(m3)
}