Threshold knot selection for large-scale spatial models with applications to the Deepwater Horizon disaster

ABSTRACT

Large spatial datasets are typically modelled through a small set of knot locations; often these locations are specified by the investigator by arbitrary criteria. Existing methods of estimating the locations of knots assume their number is known a priori, or are otherwise computationally intensive. We develop a computationally efficient method of estimating both the location and number of knots for spatial mixed effects models. Our proposed algorithm, Threshold Knot Selection (TKS), estimates knot locations by identifying clusters of large residuals and placing a knot in the centroid of those clusters. We conduct a simulation study showing TKS in relation to several comparable methods of estimating knot locations. Our case study utilizes data of particulate matter concentrations collected during the course of the response and clean-up effort from the 2010 Deepwater Horizon oil spill in the Gulf of Mexico.

Keywords:

• Fixed rank kriging
• knot selection
• reduced rank spatial model
• spatial mixed effects

Acknowledgments

In addition to the editorial staff of the Journal of Statistical Computation and Simulation and the peer reviewers, the authors thank Drs. Rajib Paul, Lawrence S. Engel, Patrica Stewart, and Mark Stenzel. All of these individuals provided suggestions which substantially improved the content and presentation of this work. The Threshold Knot Selection algorithm has been implemented in the R programming language [33]. The code for TKS is available at https://github.com/jelsema/RRSM. Should the link deprecate, contact the first author for information regarding how to obtain the code. 

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported (in part) by the Intramural Research Program of the NIH, National Institute of Environmental Health Sciences (Z01 ES101744 and ZO1 ES102945) and the NIH Common Fund.