The Fisher information function and scoring in binary ideal point item response models: a cautionary tale

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Binary ideal point item response models often exhibit bimodal Fisher information functions (FIMs) at the ideal point.
• This bimodal property can lead to indeterminacy and violations of likelihood regularity conditions.

Purpose of the Study:

• To examine the properties of Fisher information functions in binary ideal point item response models.
• To explore the implications of these properties for model scoring and estimation.

Main Methods:

• Theoretical analysis of Fisher information functions for ideal point item response models.
• Investigation of model indeterminacy and regularity condition violations.

Main Results:

• Fisher information functions in ideal point models are inherently bimodal or indeterminate.
• These properties violate standard likelihood regularity conditions, affecting asymptotic inference.
• Some models resolve indeterminacy but still violate regularity conditions; others show diverging FIMs.

Conclusions:

• Ideal point item response models possess inherent Fisher information properties that necessitate caution in their application.
• Asymptotic methods may be unreliable, especially for shorter assessments.
• Recommended scoring methods include simulated plausible values or Bayesian estimation.