An Empirical Study of Statistical Properties of Variance Partition Coefficients for Multi-Level Logistic Regression Models |
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| Authors: | Jialiang Li Brian R. Gray Douglas M. Bates |
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| Affiliation: | 1. Department of Statistics &2. Applied Probability , National University of Singapore , Singaporestalj@nus.edu.sg;4. Upper Midwest Environmental Sciences Center, U.S. Geological Survey , La Crosse, Wisconsin, USA;5. Department of Statistics , University of Wisconsin , Madison, Wisconsin, USA |
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| Abstract: | Partitioning the variance of a response by design levels is challenging for binomial and other discrete outcomes. Goldstein (2003 Goldstein , H. ( 2003 ). Multilevel Statistical Models. 3rd ed . London : Edward Arnold . [Google Scholar]) 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. |
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| Keywords: | Empirical distribution Laplacian approximation Multi-level logistic models Variance partition coefficients |
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