Spatial Extension of the Mixed Models of the Analysis of Variance

This paper proposes a spatial extension of the mixed models of the analysis of variance(MANOVA) models, which are called mixed spatial ANOVA (MS-ANOVA) models. MS-ANOVA models have been used to evaluate spatial correlations between random effects in multilevel data which is a kind of cluster data in which observations belong to some kinds of nested clusters. Because the proposed model can be regarded as a Bayesian hierarchical models, we have introduced empirical Bayesian estimation methods in which hyper parameters are estimated by quasi-maximum likelihood estimation methods in the first step and posterior distributions for the parameters are evaluated with the estimated hyper-parameters in the second step. Moreover, we have justified the asymptotic properties of the first step estimators. The proposed models are applied to happiness survey data in Japan and empirical results show that social capital which can be interpreted as "the beliefs and norms by which a community values collective action and pursues activities worthy for the entire community" significantly increases people's happiness, even after controlling for a variety of individual characteristics and spatial correlations.