Identifiability analysis of the fixed-effects one-parameter logistic positive exponent model.

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• The logistic positive exponent (LPE) model extends the two-parameter logistic (2PL) model by including an item parameter for asymmetric item characteristic curves.
• While LPE models show empirical utility, their formal identifiability has not been established.
• Item response theory (IRT) models require identifiability analysis to ensure parameter estimation is valid.

Purpose of the Study:

• To formalize the unidentified status of fixed-effects IRT models, including LPE variants.
• To conduct an identifiability analysis of the 1PL-LPE model, a specific version of the LPE model.
• To explore practical applications and implications for other LPE model versions.

Main Methods:

• Formalizing the conditions for non-identifiability in a class of fixed-effects IRT models.
• Performing a detailed identifiability analysis on the 1PL-LPE model.
• Discussing strategies for addressing identifiability issues.

Main Results:

• The 1PL-LPE model, based on the one-parameter logistic model (1PL), is demonstrated to be not identifiable.
• A broad class of fixed-effects IRT models, including LPE models, are shown to have unidentified status.
• The study provides insights into the conditions leading to non-identifiability.

Conclusions:

• The 1PL-LPE model, as formulated, is not identifiable and requires adjustments for practical use.
• Understanding model identifiability is crucial for the valid application of advanced IRT models like LPE.
• Further research can explore modifications to LPE models to ensure identifiability and utility.