sirt (version 1.5-0)

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 $\lambda_{ik}$ parameter to be estimated

min.g

Minimum $g_{pk}$ parameter to be estimated

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

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

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 <- gom.jml(dat,K=2 , maxiter=10 )
summary(m2)

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