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A clarification of the phi mixing model

M Altmann1, M Morris

  • 1Division of Health Computer Sciences, University of Minnesota, Minneapolis.

Mathematical Biosciences
|November 1, 1994
PubMed
Summary

This study critiques a deterministic model for analyzing pairwise interaction data in contingency tables. It highlights issues like non-unique decomposition and lack of statistical basis, proposing generalized linear models as a superior alternative.

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Area of Science:

  • Statistics
  • Data Analysis
  • Biostatistics

Background:

  • Analysis of two-way contingency tables is crucial for understanding pairwise interactions.
  • A deterministic model has been proposed, decomposing interaction counts into selective and random components.

Purpose of the Study:

  • To critically review the proposed deterministic model for analyzing contingency tables of pairwise interactions.
  • To identify inherent problems within the deterministic model's framework.
  • To propose a suitable alternative for analyzing such data.

Main Methods:

  • Review and critique of a deterministic model for contingency table analysis.
  • Identification of issues related to non-unique decomposition, parameter estimation, and hypothesis testing.
  • Exploration of generalized linear models as an alternative approach.

Main Results:

  • The deterministic model suffers from non-unique decomposition, hindering parameter estimation and interpretation.
  • The deterministic framework lacks a foundation for statistical estimation and hypothesis testing.
  • The assumption of decomposibility is not supported by empirical or theoretical evidence.

Conclusions:

  • The reviewed deterministic model is problematic for analyzing pairwise interaction data in contingency tables.
  • Generalized linear models offer a more statistically sound and flexible alternative.
  • Proper specification of the probability process and removal of overparameterization are key for effective analysis.

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