search.model_within: Search for the global maximum of the log-likelihood of...

In MLCIRTwithin: Latent Class Item Response Theory (LC-IRT) Models under Within-Item Multidimensionality

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)

MLCIRTwithin documentation built on Sept. 30, 2019, 5:04 p.m.