search.model_within {MLCIRTwithin}

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

Description

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

Usage

search.model_within(S, yv = rep(1, ns), kv1, kv2, X = NULL, 
                    link = c("global","local"), disc = FALSE, difl = FALSE, 
                    multi1, multi2, fort = FALSE, tol1 = 10^-6, tol2 = 10^-10,
                    glob = FALSE, disp = FALSE, output = FALSE, out_se = FALSE, 
                    nrep = 2, Zth1 = NULL, zth1 = NULL, Zth2=NULL, zth2=NULL, 
                    Zbe=NULL, zbe=NULL, Zga1=NULL, zga1=NULL, Zga2=NULL, 
                    zga2=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

kv1

vector of the possible numbers of ability levels (or latent classes) for the 1st latent variable

kv2

vector of the possible numbers of ability levels (or latent classes) for the 2nd latent variable

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)

multi1

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 1st latent variable

multi2

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 2nd 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 convergence)

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

Zth1

matrix for the specification of constraints on the support points for the 1st latent variable

zth1

vector for the specification of constraints on the support points for the 1st latent variable

Zth2

matrix for the specification of constraints on the support points for the 2nd latent variable

zth2

vector for the specification of constraints on the support points for the 2nd latent variable

Zbe

matrix for the specification of constraints on the item difficulty parameters

zbe

vector for the specification of constraints on the item difficulty parameters

Zga1

matrix for the specification of constraints on the item discriminating indices for the 1st latent variable

zga1

vector for the specification of constraints on the item discriminating indices for the 1st latent variable

Zga2

matrix for the specification of constraints on the item discriminating indices for the 2nd latent variable

zga2

vector for the specification of constraints on the item discriminating indices for the 2nd latent variable

Value

out.single

output of each single model for each k in kv1 and kv2; it is similar to output from est_multi_poly_within, with the addition of values of number of latent classes for the 1st latent variable (k1) and the 2nd latent variable (k2) 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 kv1 and kv2

bicv

Bayesian Information Criterion index for each k in kv1 and kv2

entv

Entropy index for each k in kv1 and kv2

necv

NEC index for each k in kv1 and kv2

lkv

log-likelihood at convergence of the EM algorithm for each k in kv1 and kv2

errv

trace of any errors occurred during the estimation process for each k in kv1 and kv2

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 the model under different within-item multidimensional structures
# for SF12_nomiss data
data(SF12_nomiss)
S = SF12_nomiss[,1:12]
X = SF12_nomiss[,13]

# Partial credit model with two latent variables sharing six items 
# (free difficulty parameters and constrained discriminating parameters; 
# 1 to 3 latent classes for the 1st latent variable and 1 to 2 classes for the 2nd latent variable; 
# one covariate):
multi1 = c(1:5, 8:12)
multi2 = c(6:12, 1)
out1 = search.model_within(S=S,kv1=1:3,kv2=1:2,X=X,link="global",disc=FALSE,
                             multi1=multi1,multi2=multi2,disp=TRUE,
                             out_se=TRUE,tol1=10^-4, tol2=10^-7, nrep=1)
                             
# Main output
out1$lkv 
out1$aicv
out1$bicv 
# Model with 2 latent classes for each latent variable
out1$out.single[[4]]$k1 
out1$out.single[[4]]$k2 
out1$out.single[[4]]$Th1          
out1$out.single[[4]]$Th2 
out1$out.single[[4]]$piv1 
out1$out.single[[4]]$piv2   
out1$out.single[[4]]$ga1c
out1$out.single[[4]]$ga2c   
out1$out.single[[4]]$Bec            

## End(Not run)