A unified skew-normal geostatistical factor model

The classical linear model of coregionalization and its simpler counterpart known as the proportional covariance model, or intrinsic correlation model, have become standard tools in many areas of application for the analysis of multivariate spatial data. Despite the merits of this model, it guarantees optimal predictions only in the case of Gaussian data and can lead to erroneous conclusions in all other circumstances, in particular in the presence of skew data. To deal with multivariate geostatistical data showing some degree of skewness, this article proposes a latent spatial factor model in which all finite-dimensional marginal distributions are multivariate unified skew-normal. For this model, we can write the log-likelihood function of the data and implement a maximum likelihood estimation procedure which enables the simultaneous estimation of all parameters of the model. Moreover, we also show how the computational burden involved in the nonlinear mapping of the latent factors can be substantially reduced by exploiting a linearity property of the predictions. The sampling performances of the inferential procedures are investigated in some thorough simulation studies, and an application to radioactive contamination data is presented to show the flexibility of the model. Detailed derivations of our results are available as Supplementary Material.