Spatial mixed effects model for compositional data with applications to coal geology

•We derive lognormal kriging and block kriging equations.•We extend the SME model to multivariate analysis.•We show a log-normal approach to compositional data analysis.•The implementation of our methods is illustrated on coal geochemical data.•There is higher precision when estimating block averages than individual locations.

We analyze data on the geochemical make-up of coal samples throughout the state of Illinois. The goal is to estimate the geochemical properties at unobserved locations over a specified region. Multivariate spatial modeling requires characterization of both spatial and cross-spatial covariances. Reduced rank spatial models are popular in analyzing large spatial datasets. We develop a multivariate spatial mixed effects model for log-normal processes and show how to implement with compositional data to predict on point locations, as well as the average prediction over a finite area. We use log-normal kriging for the components of compositional data, and show how to obtain estimates and measures of precision in isometric log-ratio coordinates.