Bayesian Correlated Factor Analysis for Spatial Data
نویسنده
چکیده
A hierarchical Bayesian factor model for multivariate spatially correlated data is proposed. The idea behind the proposed method is to search factor scores incorporating a dependence due to a geographical structure. The great exibility of the Bayesian approach bears directly on the problem of parameter identi cation in factor analysis and furthermore on the inclusion of our prior opinion about adjacent regions having high correlated observable and latent variables. The underling idea taken from Rowe (1998) is the introduction of separable covariance matrix for the observation vector X ′ = (x1, x2, . . . , xN), (N × p vector where N is the number of observations and p number of variables) so that var(X) = Φ ⊗ Ψ where ⊗ denotes the Kronecker product. The advantage of introducing a separable covariance matrix is that we can now interpret the matrix Φ as the between-observations covariance matrix, and the matrix Ψ as the within-observations covariance matrix. In the paper, different prior distributions for Φ, the between-observations covariance matrix, are investigated and both informative and uninformative priors are expored. High correlation between regions can be due to geographic distance or cultural af nity. The model extends a methodology for temporal dependence pattern proposed by Mezzetti and Billari (2005). A Gibbs sampling algorithm is implemented to sample from the posterior distributions. The methodology will be illustrated through the analysis of epidemiological data.
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تاریخ انتشار 2006