gom.jml.Rd
This function estimates the grade of membership model employing a joint maximum likelihood estimation method (Erosheva, 2002; p. 23ff.).
gom.jml(dat, K=2, seed=NULL, globconv=0.001, maxdevchange=0.001, maxiter=600, min.lambda=0.001, min.g=0.001)
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 |
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 |
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 $$ P(X_{pi}=1 | g_{p1}, \ldots, g_{pK} )=\sum_k \lambda_{ik} g_{pk} \quad, \quad \sum_k g_{pk}=1 $$
A list with following entries:
Data frame of item parameters \(\lambda_{ik}\)
Data frame of individual membership scores \(g_{pk}\)
Mean membership scores
Discretized membership scores
Distribution of discretized membership scores
Number of classes
Deviance
Information criteria
Number of students
Person score
Number of iterations
List with processed data (recoded data, starting values, ...)
Further values
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.
S3 method summary.gom
############################################################################# # 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) }