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Titolo:
SOME ALGEBRA AND GEOMETRY FOR HIERARCHICAL-MODELS, APPLIED TO DIAGNOSTICS
Autore:
HODGES JS;
Indirizzi:
UNIV MINNESOTA,DIV BIOSTAT,SUITE 200,2221 UNIV AVE MINNEAPOLIS MN 55414
Titolo Testata:
Journal of the Royal Statistical Society. Series B: Methodological
, volume: 60, anno: 1998,
parte:, 3
pagine: 497 - 521
SICI:
1369-7412(1998)60:<497:SAAGFH>2.0.ZU;2-T
Fonte:
ISI
Lingua:
ENG
Soggetto:
POPULATION PHARMACOKINETIC MODELS; LINEAR-MODEL; REGRESSION-ANALYSIS; BAYESIAN-ANALYSIS; GIBBS SAMPLER; MIXED MODELS; VARIANCE; PLOTS; COMPONENTS;
Keywords:
BAYESIAN METHODS; DYNAMIC LINEAR MODELS; MULTILEVEL MODELS; RANDOM EFFECT MODELS; SPATIAL DATA; TIME VARYING REGRESSION; VARIANCE COMPONENTS;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
CompuMath Citation Index
Science Citation Index Expanded
Citazioni:
71
Recensione:
Indirizzi per estratti:
Citazione:
J.S. Hodges, "SOME ALGEBRA AND GEOMETRY FOR HIERARCHICAL-MODELS, APPLIED TO DIAGNOSTICS", Journal of the Royal Statistical Society. Series B: Methodological, 60, 1998, pp. 497-521

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 anapproach 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.

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Documento generato il 02/12/20 alle ore 16:35:23