Unidimensionality in Rasch Models: Efficient Item Selection and Hierarchical Clustering Methods Based on Marginal Estimates

TL;DR

This paper introduces an efficient method for selecting Rasch model items based on marginal estimates of the standard deviation of the mixing distribution, and proposes hierarchical clustering to identify item groups sharing a common trait.

Contribution

It presents a novel item selection procedure using marginal estimates and extends it with hierarchical clustering for trait grouping, improving Rasch model item analysis.

Findings

Selection procedure is highly reliable on average.

A criterion effectively identifies non-Rasch items.

Hierarchical clustering works well as an exploratory tool.

Abstract

A strong tool for the selection of items that share a common trait from a set of given items is proposed. The selection method is based on marginal estimates and exploits that the estimates of the standard deviation of the mixing distribution are rather stable if items are from a Rasch model with a common trait. If, however, the item set is increased by adding items that do not share the latent trait the estimated standard deviations become distinctly smaller. A method is proposed that successively increases the set of items that are considered Rasch items by examining the estimated standard deviations of the mixing distribution. It is demonstrated that the selection procedure is on average very reliable and a criterion is proposed, which allows to identify items that should not be considered Rasch items for concrete item sets. An extension of the method allows to investigate which groups of items might share a common trait. The corresponding hierarchical clustering procedure is considered an exploratory tool but works well on average.