Evaluating Manifest Monotonicity Using Bayes Factors.

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Assessing latent monotonicity in item response theory (IRT) for dichotomous data is challenging as it cannot be directly evaluated.
• Manifest monotonicity serves as an observable consequence to infer latent monotonicity.
• Current methods for manifest monotonicity evaluation primarily focus on falsification, offering only indirect evidence.

Purpose of the Study:

• To introduce Bayes factors as a method for quantifying evidence in favor of or against manifest monotonicity.
• To extend the use of Bayes factors with informative hypotheses to compare manifest monotonicity against relevant alternatives.
• To provide a flexible procedure for assessing manifest monotonicity in real-world psychometric data.

Main Methods:

• Utilizing Bayes factors to calculate the degree of support for manifest monotonicity.
• Employing informative hypotheses to compare manifest monotonicity against substantive or statistical alternatives.
• Evaluating the proposed procedure through a simulation study and application to empirical data.

Main Results:

• The simulation study demonstrated the performance of the Bayes factor procedure in assessing manifest monotonicity.
• The application to empirical data illustrated the practical utility of the proposed method.
• Bayes factors provide a direct measure of evidence, unlike traditional falsification-based approaches.

Conclusions:

• Bayes factors offer a robust and flexible approach to evaluate manifest monotonicity in item response theory.
• This method enhances the assessment of latent monotonicity assumptions in psychometric analyses.
• The procedure facilitates a more nuanced understanding of model fit by comparing competing hypotheses.