chapter  32
Smoothed ANOVA Modeling
ByMiguel A. Martinez-Beneito, James S. Hodges, and Marc Mar´ı-Dell’Olmo
Pages 14

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, Scheffe´ [4]. Zhang et al. [5] applied this approach to multivariate disease mapping as a

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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 Mar´ı-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.