Item Response Theory Models for Carry-Over Effect Across Different Scales

Area of Science:

• Psychometrics
• Educational Measurement
• Psychological Assessment

Background:

• Surveys and tests often require judging single statements across multiple scales.
• This practice can introduce local dependence due to the same statement influencing subsequent responses.
• Existing item response theory (IRT) models may not adequately capture this specific type of dependence.

Purpose of the Study:

• To develop a new class of item response theory (IRT) models.
• To account for nonrecursive carry-over effects in multi-scale judgments.
• To evaluate the performance of these new models and compare them to standard IRT models.

Main Methods:

• Development of novel IRT models incorporating nonrecursive carry-over effects.
• Parameter estimation using the WinBUGS freeware.
• Two simulation studies to assess parameter recovery and model misspecification consequences.
• Analysis of empirical data from parallel and sequential designs.

Main Results:

• New IRT models demonstrated good parameter recovery in simulations.
• Fitting unnecessarily complex models had minimal negative impact.
• Ignoring carry-over effects led to biased estimates in item parameters, latent trait correlations, and reliability when using standard IRT models.
• Empirical examples illustrated the practical application of the new models.

Conclusions:

• The proposed IRT models effectively capture nonrecursive carry-over effects in multi-scale judgments.
• Failure to account for these effects can bias key psychometric estimates.
• These models offer improved accuracy for analyzing data from educational and psychological assessments with multi-scale items.