Investigating the Ordering Structure of Clustered Items Using Nonparametric Item Response Theory

Area of Science:

• Psychometrics
• Educational Measurement
• Psychological Testing

Background:

• Ordered item structures in educational and psychological tests enhance administration and interpretation.
• The validity of such tests heavily depends on the strength of their ordering structure.
• Existing methods may not fully capture the nuances of ordering in clustered item sets.

Purpose of the Study:

• To define and evaluate three types of order invariance for clustered item sets: weak invariant cluster ordering, strong invariant cluster ordering, and clustered invariant item ordering.
• To propose a nonparametric item response theory (IRT) procedure for assessing this order invariance.
• To provide a framework for validating the ordering structure of measurement instruments with clustered items.

Main Methods:

• Utilizing a nonparametric item response theory (IRT) approach.
• Implementing a procedure based on local assessment of pairwise conditional expectations at cluster and item levels.
• Employing global assessment of Guttman errors using generalized H-coefficients for item-cluster contexts.

Main Results:

• A novel procedure for evaluating the three-fold continuum of order invariance in clustered item sets is presented.
• The procedure integrates local and global assessment methods for robust evaluation.
• The methodology is demonstrated through an empirical example and implemented in R.

Conclusions:

• The proposed IRT procedure offers a validated method for assessing the ordering structure of clustered measurement instruments.
• This framework supports improved test construction, administration, and score interpretation.
• Further research and methodological developments are suggested for advancing psychometric practices.