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Titolo: SOME ALGEBRA AND GEOMETRY FOR HIERARCHICALMODELS, 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:
 13697412(1998)60:<497:SAAGFH>2.0.ZU;2T
 Fonte:
 ISI
 Lingua:
 ENG
 Soggetto:
 POPULATION PHARMACOKINETIC MODELS; LINEARMODEL; REGRESSIONANALYSIS; BAYESIANANALYSIS; 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 HIERARCHICALMODELS, APPLIED TO DIAGNOSTICS", Journal of the Royal Statistical Society. Series B: Methodological, 60, 1998, pp. 497521
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 terrors. 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 reexpression 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