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Partitioning variation in multilevel models for count data.

George Leckie1, William J Browne1, Harvey Goldstein1

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This study introduces new methods for calculating variance partition coefficients (VPCs) and intraclass correlation coefficients (ICCs) for multilevel models with count data. These methods address challenges with categorical and overdispersed count responses, improving the analysis of clustered data.

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Area of Science:

  • Multilevel modeling
  • Statistical analysis of clustered data
  • Count response models

Background:

  • Calculating variance partition coefficients (VPCs) and intraclass correlation coefficients (ICCs) is crucial for understanding clustering in multilevel models.
  • Existing methods for VPC/ICC calculation are challenging for categorical and count response models.
  • Lack of guidance leads to inadequate reporting of clustering effects in applied research.

Purpose of the Study:

  • To derive exact VPC/ICC expressions for multilevel models with negative binomial and Poisson count responses.
  • To extend these expressions to three-level and random-coefficient models.
  • To provide guidance for applied researchers on quantifying clustering in count data.

Main Methods:

  • Derivation of exact algebraic expressions for VPCs/ICCs for negative binomial models.
  • Extension of these derivations to three-level models.
  • Application of derived methods to a real-world dataset on student absenteeism.

Main Results:

  • Exact VPC/ICC expressions are provided for flexible negative binomial models, accounting for overdispersion.
  • The study presents VPC/ICC expressions for three-level and random-coefficient extensions.
  • The methods are demonstrated effectively using an example of student absenteeism data.

Conclusions:

  • The derived exact VPC/ICC expressions facilitate better assessment of clustering in multilevel count models.
  • These methods address limitations of previous approaches for categorical and count data.
  • The findings empower researchers to more accurately report and interpret the importance of cluster effects.