Mixture of Regression Models for Large Spatial Datasets

Type
Article

Authors
Kazor, Karen
Hering, Amanda S.

KAUST Grant Number
CRG2015-2582

Date
2019-06-17

Abstract
When a spatial regression model that links a response variable to a set of explanatory variables is desired, it is unlikely that the same regression model holds throughout the domain when the spatial domain and dataset are both large and complex. The locations where the trend changes may not be known, and we present here a mixture of regression models approach to identifying the locations wherein the relationship between the predictors and the response is similar; to estimating the model within each group; and to estimating the number of groups. An EM algorithm for estimating this model is presented along with a criterion for choosing the number of groups. Performance of the estimators and model selection are demonstrated through simulation. An example with groundwater depth and associated predictors generated from a large physical model simulation demonstrates the fit and interpretation of the proposed model. R code is provided in the supplementary materials that simulates the scenarios tested herein; implements the method; and reproduces the groundwater depth results. Supplementary materials for this article are available online.

Citation
Kazor, K., & Hering, A. S. (2019). Mixture of Regression Models for Large Spatial Datasets. Technometrics, 61(4), 507–523. doi:10.1080/00401706.2019.1569558

Acknowledgements
This research was partially supported by the National Science Foundation under Cooperative Agreement EEC-1028969 (ERC/ReNUWIt); the State of Colorado through the Higher Education Competitive Research Authority; and King Abdullah University of Science and Technology through CRG2015-2582.

Publisher
AMER STATISTICAL ASSOC

Journal
TECHNOMETRICS

DOI
10.1080/00401706.2019.1569558

Additional Links
https://www.tandfonline.com/doi/full/10.1080/00401706.2019.1569558

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