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.
|Original language||English (US)|
|Number of pages||17|
|State||Published - Jun 17 2019|
Bibliographical noteKAUST Repository Item: Exported on 2022-06-07
Acknowledged KAUST grant number(s): CRG2015-2582
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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Modeling and Simulation
- Applied Mathematics
- Statistics and Probability