search.model_between {MLCIRTwithin}

Search for the global maximum of the log-likelihood of between-item muldimensional models

Description

It searches for the global maximum of the log-likelihood of between-item muldimensional models given a vector of possible number of classes to try for.

Usage

search.model_between(S, yv = rep(1, ns), kv, X = NULL,
                     link = c("global","local"), disc = FALSE, difl = FALSE,
                     multi = 1:J, fort = FALSE, tol1 = 10^-6, tol2 = 10^-10,
                     glob = FALSE, disp = FALSE, output = FALSE,
                     out_se = FALSE, nrep = 2, Zth=NULL,zth=NULL,
                     Zbe=NULL, zbe=NULL,Zga=NULL,zga=NULL)

Arguments

S

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

yv

vector of the frequencies of every response configuration in S

kv

vector of the possible numbers of latent classes

X

matrix of covariates affecting the weights

link

type of link function ("global" for global logits, "local" for local logits); with global logits a graded response model results; with local logits a partial credit model 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 (FALSE = all equal to one, TRUE = free)

difl

indicator of constraints on the difficulty levels (FALSE = free, TRUE = 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 for the latent variable

fort

to use Fortran routines when possible

tol1

tolerance level for checking convergence of the algorithm as relative difference between consecutive log-likelihoods (initial check based on random starting values)

tol2

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

glob

to use global logits in the covariates

disp

to display the likelihood evolution step by step

output

to return additional outputs (Piv,Pp,lkv)

out_se

to return standard errors

nrep

number of repetitions of each random initialization

Zth

matrix for the specification of constraints on the support points

zth

vector for the specification of constraints on the support points

Zbe

matrix for the specification of constraints on the item difficulty parameters

zbe

vector for the specification of constraints on the item difficulty parameters

Zga

matrix for the specification of constraints on the item discriminating indices

zga

vector for the specification of constraints on the item discriminating indices

Value

out.single

output of each single model for each k in kv; it is similar to output from est_multi_poly_between, with the addition of values of number of latent classes (k) and the sequence of log-likelihoods (lktrace) for the deterministic start, for each random start, and for the final estimation obtained with a tolerance level equal to tol2

aicv

Akaike Information Criterion index for each k in kv

bicv

Bayesian Information Criterion index for each k in kv

entv

Entropy index for each k in kv

necv

NEC index for each k in kv

lkv

log-likelihood at convergence of the EM algorithm for each k in kv

errv

trace of any errors occurred during the estimation process for each k in kv

Author(s)

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

References

Bartolucci, F., Bacci, S. and Gnaldi, M. (2014), MultiLCIRT: An R package for multidimensional latent class item response models, Computational Statistics & Data Analysis, 71, 971-985.

Examples

## Not run: 
# Fit a Graded response model with two latent variables (free discrimination
# and difficulty parameters; two latent classes):
data(SF12_nomiss)
S = SF12_nomiss[,1:12]
X = SF12_nomiss[,13]
multi0 = rbind(c(1:5, 8), c(6:7,9:12))
out1 = search.model_between(S=S,kv=1:3,X=X,link="global",disc=TRUE,
                               multi=multi0,fort=TRUE,disp=TRUE,out_se=TRUE) 

# Display output
out1$lkv
out1$bicv

# Display output with 2 classes:
out1$out.single[[2]]
out1$out.single[[2]]$lktrace
out1$out.single[[2]]$Th
out1$out.single[[2]]$piv
out1$out.single[[2]]$gac
out1$out.single[[2]]$Bec


## End(Not run)