A Characterization of Monotone Unidimensional Latent Variable Models

A Characterization of Monotone Unidimensional Latent Variable Models

A note on monotone likelihood ratio of the total score variable in unidimensional item response theory.

This note provides a direct, elementary proof of the fundamental result on monotone likelihood ratio of the total score variable in unidimensional item response theory (IRT). This result is very important for practical measurement in IRT, because it justifies the use of the total score variable to order participants on the latent trait. The proof relies on a basic inequality for elementary symm...

Nonparametric IRT: Scoring functions and ordinal parameter estimation of isotonic probabilistic models (ISOP)

The most popular unidimensional psychological test evaluation rule is the trivial scoring function: To the answers of each item of a test item scores of 0,1,...m points are awarded and the unweighted or simple or total sum of the item scores gives the test score (also: Likert score). This total score has desirable stochastic ordering properties like monotone likelihood ratio (MLR), stochastic o...

The Comparison of Two Models for Evaluation of Pre-internship Comprehensive Test: Classical and Latent Trait

Introduction: Despite the widespread use of pre-internship comprehensive test and its importance in medical students’ assessment, there is a paucity of the studies that can provide a systematic psychometric analysis of the items of this test. Thus, the present study sought to assess March 2011 pre-internship test using classical and latent trait models and compare their results. Methods: In th...

Model-based multidimensional clustering of categorical data

Existing models for cluster analysis typically consist of a number of attributes that describe the objects to be partitioned and one single latent variable that represents the clusters to be identified. When one analyzes data using such a model, one is looking for one way to cluster data that is jointly defined by all the attributes. In other words, one performs unidimensional clustering. This ...