Title: Estimating the Joint Item-Score Density Using an Unrestricted Latent
Class Model: Advancing Flexibility in Computerized Adaptive Testing

Authors: Anastasios Psychogyiopoulos, Niels Smits, L. Andries van der Ark

Abstract:
Computer adaptive testing (CAT) shortens test duration without affecting
measurement accuracy, hence preventing biased evaluation and incorrect or
inefficient treatment. However, the assumptions of item-response theory
models—commonly used in CAT—may be too stringent for some tests. This study
investigates the bias and accuracy of a flexible CAT procedure, coined LSCAT
(for latent-class sum-score CAT). In the calibration phase, an unrestricted
latent class model estimates the joint item-score density (π) and the
total-score density (π+); in the operational phase, the respondents’ expected
sum scores are estimated. The paper’s first study indicates that using the
Bayesian Information Criterion (BIC) to determine the number of latent classes
produces the most accurate estimates of π and π+. The second study shows that
the unrestricted latent class model more accurately estimates π and π+ than
the two-parameter logistic model, especially under a complex data-generating
mechanism. As a proof of concept, the third study compared the efficiency of
LSCAT and a traditional CAT procedure using the two-parameter logistic model
using a single empirical data set. The two CAT procedures were approximately
equally efficient, yet LSCAT was more efficient for the high- and low-scoring
respondents, while less efficient for respondents in the middle.

Keywords: Computer adaptive testing, item-calibration, latent class analysis,
model selection, density-estimation, CAT simulation