MultiLCIRT (version 2.11)

class_item: Hierarchical classification of test items

Description

It performs a hierarchical classification of a set of test items on the basis of the responses provided by a sample of subjects. The classification is based on a sequence of likelihood ratio tests between pairs of multidimensional models suitably formulated.

Usage

class_item(S, yv, k, link = 1, disc = 0, difl = 0, fort = FALSE,
           disp = FALSE, tol = 10^-10)

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

k

number of ability levels (or latent classes)

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)

fort

to use fortran routines when possible

disp

to display the likelihood evolution step by step

tol

tolerance level for convergence

Value

merge

input for the dendrogram represented by the R function plot

height

input for the dendrogram represented by the R function plot

lk

maximum log-likelihood of the model resulting from each aggregation

np

number of free parameters of the model resulting from each aggregation

lk0

maximum log-likelihood of the latent class model

np0

number of free parameters of the latent class model

groups

list of groups resulting (step-by-step) from the hierarchical clustering

dend

hclust object to represent the histogram

call

command used to call the function

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

## Model-based hierarchical classification of items from simulated data
# Setup
r = 6  # number of items
n = 1000  # sample size
bev = rep(0,r) 
k = r/2
multi = rbind(1:(r/2),(r/2+1):r)
L = chol(matrix(c(1,0.6,0.6,1),2,2))
data = matrix(0,n,r)
model = 1 
# Create data
Th = matrix(rnorm(2*n),n,2)<!-- %*%L    -->
for(i in 1:n) for(j in 1:r){
	if(j<=r/2){
    	pc = exp(Th[i,1]-bev[j]); pc = pc/(1+pc)
	}else{
		pc = exp(Th[i,2]-bev[j]); pc = pc/(1+pc)
    }
    data[i,j] = runif(1)<pc
}
# Aggregate data
out = aggr_data(data)
S = out$data_dis
yv = out$freq
# Create dendrogram for items classification, by assuming k=3 latent
# classes and a Rasch parameterization
out = class_item(S,yv,k=3,link=1)
summary(out)
plot(out$dend)



## Model-based hierarchical classification of NAEP items
# Aggregate data
data(naep)
X = as.matrix(naep)
out = aggr_data(X)
S = out$data_dis
yv = out$freq
# Create dendrogram for items classification, by assuming k=4 latent
# classes and a Rasch parameterization
out = class_item(S,yv,k=4,link=1)   
summary(out)
plot(out$dend)