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How to Assess a Model's Testability and Identifiability.

Bamber1, van Santen JP

  • 1Space & Naval Warfare Systems Center, San Diego

Journal of Mathematical Psychology
|March 29, 2000
PubMed
Summary

This study defines quantitative testability and identifiability for models, introducing rules like the Jacobian Rule to assess model reliability when parameters cannot be directly observed.

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Area of Science:

  • Mathematical Modeling
  • Systems Analysis
  • Statistical Inference

Background:

  • Models are essential in science, but their reliability depends on precise predictions and parameter ascertainment.
  • Intuitive concepts of model testability and identifiability lack formal definitions, leading to potential misinterpretations.

Purpose of the Study:

  • To provide formal definitions for quantitative testability, identifiability, and redundancy in models.
  • To examine and refine rules of thumb for assessing model properties, particularly the Counting Rule and its generalization, the Jacobian Rule.

Main Methods:

  • Formal definitions of model testability, identifiability, and redundancy are established.
  • The Counting Rule and the Jacobian Rule are analyzed for their applicability to quantitatively testable and identifiable models.
  • The Identifiability Rule is presented for assessing model identifiability.
  • Linear and discrete-state models are used to illustrate the application of these rules.

Main Results:

  • A model is quantitatively testable if its predictions are precise and narrow.
  • A model is identifiable if its parameters can be determined from empirical data.
  • The Counting Rule for testability is valid only for identifiable models.
  • The Jacobian Rule generalizes the Counting Rule for unidentifiable models, using the rank of the Jacobian matrix.
  • The Identifiability Rule uses the Jacobian matrix rank to determine if a model is identifiable.

Conclusions:

  • Formal definitions and rules enhance the rigorous assessment of model quantitative testability and identifiability.
  • The Jacobian Rule provides a more robust method for assessing quantitative testability, especially for unidentifiable models.
  • While these rules offer strong indications, definitive conclusions require further in-depth analysis.

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