Metric Transformations and the Filtered Monotonic Polynomial Item Response Model.

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• The standard theta metric in item response theory (IRT) can be limiting for practical score reporting and interpretation.
• Nonparametric item response models offer greater flexibility in capturing complex item response functions.

Purpose of the Study:

• To demonstrate that the filtered monotonic polynomial (FMP) item response model can be utilized for specifying IRT models on alternative metrics.
• To show how item response functions (IRFs) within the FMP framework can be re-expressed on different latent trait metric scales through monotonic transformations.

Main Methods:

• Derivation of item parameter transformations for both linear and nonlinear transformations of the latent trait metric.
• Utilizing monotonic polynomial approximations to link different metric scales.
• Application of the FMP model to define an IRT model directly on the approximate true score metric.

Main Results:

• Any IRF defined within the FMP framework can be re-expressed as another FMP IRF by applying monotonic transformations to the latent trait.
• Item parameter transformations allow for the specification of IRT models on various monotonic transformations of the theta metric.
• Successful definition of an IRT model directly on the approximate true score metric using the FMP framework.

Conclusions:

• The FMP model provides a versatile framework for adapting IRT models to alternative metrics, enhancing score interpretability.
• Metric transformations within the FMP model have significant implications for applied testing, allowing for more tailored score reporting.
• This approach broadens the applicability of IRT by enabling models to be defined on metrics more relevant to specific testing contexts.