A Moving Average Approach for Spatial Statistical Models of Stream Networks
Jay M. Ver Hoef
National Marine Mammal Laboratory, NOAA National Marine Fisheries Service, Fairbanks, AK, United States

This talk discusses the use of moving averages to develop new classes of models in a flexible modeling framework for stream networks. Streams and rivers are among our most important resources, yet models with autocorrelated errors for spatially-continuous stream networks have only recently been described. I develop models based on stream distance rather than Euclidean distance. Spatial autocovariance models developed for Euclidean distance may not be valid when using stream distance. I begin by describing a stream topology. I then use moving averages to build several classes of valid models for streams. Various models are derived depending on whether the moving average has a “tail-up-stream”, “tail-down-stream”, or a “two-tail” construction. These models can also account for the volume and direction of flowing water. The data for this article come from the Ecosystem Health Monitoring Program in Southeast Queensland, Australia, which is an important national program aimed at monitoring water quality. I model two water chemistry variables, pH and conductivity, for sample sizes of near 100. I estimate fixed effects and make spatial predictions. One interesting aspect of stream networks is the possible dichotomy of autocorrelation between flow-connected and flow-unconnected locations. For this reason, it is important to have a flexible modeling framework, which is achieved on the example data by using a variance component approach.

Keywords: Geostatistics; Spatial autocorrelation; Kernel convolution; Spatial linear model

Biography: Jay Ver Hoef is a statistician with the NOAA National Marine Mammal Laboratory in Seattle. He serves as a statistical consultant and continues his research interests in spatial statistics and environmental statistics. He is also an adjunct professor of statistics with the Mathematics Department of the University of Alaska, Fairbanks, and a fellow of the American Statistical Association.