search.model {MultiLCIRT}

Search for the global maximum of the log-likelihood

Description

It search for the global maximum of the log-likelihood given a vector of possible number of classes to try for.

Usage

search.model(S, yv = rep(1,ns), kv, X = NULL, link = 0, disc = 0,
             difl = 0, multi = 1:J, fort = FALSE, tol = 10^-10,
             nrep = 2, glob = FALSE, disp=FALSE)

Arguments

S

matrix of all response sequences observed at least once in the sample and listed row-by-row (use 999 for missing response)

yv

vector of the frequencies of every response configuration in S

kv

vector of the possible numbers of latent classes

X

matrix of covariates that affects the weights

link

type of link function (1 = global logits, 2 = local logits); with global logits the Graded Response model results; with local logits the Partial Credit results (with dichotomous responses, global logits is the same as using local logits resulting in the Rasch or the 2PL model depending on the value assigned to disc)

disc

indicator of constraints on the discriminating indices (0 = all equal to one, 1 = free)

difl

indicator of constraints on the difficulty levels (0 = free, 1 = rating scale parametrization)

multi

matrix with a number of rows equal to the number of dimensions and elements in each row equal to the indices of the items measuring the dimension corresponding to that row

fort

to use fortran routines when possible

tol

tolerance level for checking convergence of the algorithm as relative difference between consecutive log-likelihoods

nrep

number of repetitions of each random initialization

glob

to use global logits in the covariates

disp

to dispaly partial output

Value

out.single

output of each single model (as from est_multi_poly) for each k in kv

bicv

value of BIC index for each k in kv

lkv

value of log-likelihood for each k in kv

Author(s)

Francesco Bartolucci, Silvia Bacci, Michela Gnaldi - University of Perugia (IT)

References

Bartolucci, F. (2007), A class of multidimensional IRT models for testing unidimensionality and clustering items, Psychometrika, 72, 141-157.

Bacci, S., Bartolucci, F. and Gnaldi, M. (2012), A class of Multidimensional Latent Class IRT models for ordinal polytomous item responses, Technical report, http://arxiv.org/abs/1201.4667.

Examples

## Not run: 
## Search Multidimensional LC IRT models for binary responses
# Aggregate data
data(naep)
X = as.matrix(naep)
out = aggr_data(X)
S = out$data_dis
yv = out$freq
# Define matrix to allocate each item on one dimension 
multi1 = rbind(c(1,2,9,10),c(3,5,8,11),c(4,6,7,12))
out2 = search.model(S, yv = yv, kv=c(1:4),multi=multi1)

## End(Not run)