Smoothed ANOVA Modeling

Authored by: Miguel A. Martinez-Beneito , James S. Hodges , Marc Marí-Dell’Olmo

Handbook of Spatial Epidemiology

Print publication date:  April  2016
Online publication date:  April  2016

Print ISBN: 9781482253016
eBook ISBN: 9781482253023
Adobe ISBN:

10.1201/b19470-37

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Abstract

Smoothed analysis of variance, usually known as SANOVA, was proposed in different forms with different goals by Nobile and Green [1], Gelman [2], and Hodges et al. [3]. This chapter builds on the latter, which proposed a method for smoothing effects in balanced ANOVAs having a single error term, that is, without random effects as understood by, for example, Scheffé [4]. Zhang et al. [5] applied this approach to multivariate disease mapping as a simpler alternative to the intrinsic multivariate conditional autoregressive (MCAR) distribution, often used to analyze multivariate areal data (Section 1 of Zhang et al. [5] gives citations to pertinent MCAR literature). This application of SANOVA used specific known linear combinations of the diseases under study, presumably with particular meanings, to structure the covariance among diseases, which in most multivariate analyses is usually assumed to be unknown and unstructured [6, 7]. More recently Marí-Dell’Olmo et al. [8] proposed a reformulation of SANOVA for disease mapping that is simpler to implement and allows extensions such as multivariate ecological regression and spatiotemporal modeling.

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