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An empirical study of statistical properties of variance partition coefficients for multi-level logistic regression models

Li, J., Gray B.R., and Bates, D.M., 2008, An empirical study of statistical properties of variance partition coefficients for multi-level logistic regression models: Communications in Statistics - Simulation and Computation, v. 37, p. 2010-2026

Abstract

Partitioning the variance of a response by design levels is challenging for binomial and other discrete outcomes. Goldstein (2003) proposed four definitions for variance partitioning coefficients (VPC) under a two-level logistic regression model. In this study, we explicitly derived formulae for multi-level logistic regression model and subsequently studied the distributional properties of the calculated VPCs. Using simulations and a vegetation dataset, we demonstrated associations between different VPC definitions, the importance of methods for estimating VPCs (by comparing VPC obtained using Laplace and penalized quasilikehood methods), and bivariate dependence between VPCs calculated at different levels. Such an empirical study lends an immediate support to wider applications of VPC in scientific data analysis.

Keywords

Empirical distribution, Laplacian approximation, Multi-level logistic models, Variance partition coefficients