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A flexible count data regression model for risk analysis.

Seth D Guikema1, Jeremy P Coffelt, Jeremy P Goffelt

  • 1Department of Geography and Environmental Engineering, Johns Hopkins University, Baltimore, MD 21218, USA. sguikema@jhu.edu

Risk Analysis : an Official Publication of the Society for Risk Analysis
|February 29, 2008
PubMed
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A new Conway-Maxwell Poisson generalized linear model (COM GLM) effectively analyzes count data for risk and reliability. This model handles both underdispersed and overdispersed data, outperforming existing methods for underdispersed cases.

Area of Science:

  • Statistics
  • Reliability Engineering
  • Power Systems Analysis

Background:

  • Risk and reliability analyses frequently estimate probabilities of discrete events.
  • Explanatory variables aid in estimating future event likelihoods using regression models like generalized linear models (GLM).
  • Existing GLMs struggle with the variance structures common in count data, failing to unify under- and overdispersed data analysis.

Purpose of the Study:

  • Introduce a novel GLM based on the Conway-Maxwell Poisson (COM) distribution.
  • Address limitations of standard GLMs in handling both underdispersed and overdispersed count data.
  • Apply the new COM GLM to electric power system reliability assessment.

Main Methods:

  • Reformulated the Conway-Maxwell Poisson (COM) distribution to create a new GLM.

Related Experiment Videos

  • Applied the proposed COM GLM to analyze electric power system reliability data.
  • Compared the performance of the COM GLM against existing models for count data.

    • Main Results:

    • The proposed COM GLM effectively models both underdispersed and overdispersed count data within a single framework.
    • The COM GLM demonstrated comparable or superior data fitting compared to existing models.
    • Specifically, the COM GLM outperformed common models for underdispersed datasets.

    Conclusions:

    • The COM GLM offers a flexible and robust approach for risk and reliability analyses involving count data.
    • This new model enhances the analysis of electric power system reliability by accommodating diverse variance structures.
    • The COM GLM provides a unified framework for count data regression, improving upon limitations of standard GLMs.