Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/5156
Type: Journal article
Title: Some algebra and geometry for hierarchical models, applied to diagnostics
Author: Cox, D.
Solomon, P.
Citation: Journal of the Royal Statistical Society. Series B (Statistical Methodology), 1998; 60(3):497-536
Publisher: Wiley
Issue Date: 1998
ISSN: 0035-9246
1467-9868
Statement of
Responsibility: 
James S. Hodges
Abstract: Recent advances in computing make it practical to use complex hierarchical models. However, the complexity makes it difficult to see how features of the data determine the fitted model. This paper describes an approach to diagnostics for hierarchical models, specifically linear hierarchical models with additive normal or t-errors. The key is to express hierarchical models in the form of ordinary linear models by adding artificial `cases' to the data set corresponding to the higher levels of the hierarchy. The error term of this linear model is not homoscedastic, but its covariance structure is much simpler than that usually used in variance component or random effects models. The re-expression has several advantages. First, it is extremely general, covering dynamic linear models, random effect and mixed effect models, and pairwise difference models, among others. Second, it makes more explicit the geometry of hierarchical models, by analogy with the geometry of linear models. Third, the analogy with linear models provides a rich source of ideas for diagnostics for all the parts of hierarchical models. This paper gives diagnostics to examine candidate added variables, transformations, collinearity, case influence and residuals.
Keywords: Bayesian methods; Dynamic linear models; Multilevel models; Random effect models; Spatial data; Time varying regression; Variance component
Rights: © 1998 Royal Statistical Society
RMID: 0030006355
Published version: http://www.jstor.org/stable/2985928
Appears in Collections:Statistics publications

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