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Updated: Feb 26, 2026

Computerized Adaptive Testing System of Functional Assessment of Stroke

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Adjusted Residuals for Evaluating Conditional Independence in IRT Models for Multistage Adaptive Testing.

Peter W van Rijn¹, Usama S Ali^2,3, Hyo Jeong Shin⁴

¹ETS Global.

|February 25, 2026

Summary

This summary is machine-generated.

Item response theory (IRT) models require adjustments for multistage adaptive testing (MST) data due to routing decisions. Unadjusted residuals are inappropriate, but adjusted residuals show satisfactory Type I errors in simulations and real data analysis.

Keywords:

conditional independence item response theory multistage adaptive testing residual analysis

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Area of Science:

Psychometrics
Statistical Modeling
Educational Measurement

Background:

Item response theory (IRT) models assume conditional independence of item responses given latent ability.
Multistage adaptive testing (MST) designs involve routing decisions that can violate this conditional independence assumption.
This violation can impact statistical inference in psychometric analyses.

Purpose of the Study:

To investigate the impact of routing decisions in MST designs on the conditional independence assumption in IRT models.
To evaluate the appropriateness of generalized residuals for analyzing MST data.
To propose and validate adjustments to residuals for MST data.

Main Methods:

The study examines the quasi-independence phenomenon in the context of MST data.
It demonstrates the inapplicability of standard generalized residuals (Haberman & Sinharay, 2013) to MST data without modification.
Adjustments to residuals are developed, dependent on MST design complexity, and evaluated through simulation and real data analysis.

Main Results:

Generalized residuals for item pair frequencies are inappropriate for MST data without design-specific adjustments.
The proposed adjusted residuals demonstrate satisfactory Type I error rates in simulation studies.
The adjusted residuals were successfully applied to real MST data from the Programme for International Student Assessment (PISA).

Conclusions:

Standard IRT residual diagnostics are not directly applicable to MST data.
Adjustments to residuals are necessary and effective for valid statistical inference in MST designs.
The findings have implications for statistical inference and model fit assessment in adaptive testing environments.