Selection Criterion of Working Correlation Structure for Spatially Correlated Data

Abstract

To obtain regression parameter estimates in generalized estimation equation modeling, whether in longitudinal or spatially correlated data, it is necessary to specify the structure of the working correlation matrix. The regression parameter estimates can be affected by the choice of this matrix. Within spatial statistics, the correlation matrix also influences how spatial variability is modeled. Therefore, this study proposes a new method for selecting a working matrix, based on conditioning the variance-covariance matrix naive. The method performance is evaluated by an extensive simulation study, using the marginal distributions of normal, Poisson, and gamma for spatially correlated data. The correlation structure specification is based on semivariogram models, using the Wendland, Matérn, and spherical model families. The results reveal that regarding the hit rates of the true spatial correlation structure of simulated data, the proposed criterion resulted in better performance than competing criteria: quasi-likelihood under the independence model criterion QIC, correlation information criterion CIC, and the Rotnizky–Jewell criterion RJC. The application of an appropriate spatial correlation structure selection was shown using the first-semester average rainfall data of 2021 in the state of Pernambuco, Brazil.

Keywords:

• Condition number
• Geostatistics
• Matérn family
• Wendland covariance

Supplementary Materials

In the supplementary material we present some additional simulations results on the performance of the CNBC criterion when used in the context of longitudinal data.

Acknowledgments

The authors would like to thank the editor and referees for their comments and suggestions.

Additional information

Funding

De Bastiani would like to thank you the National Counsel of Technological and Scientific Development (CNPq) process number 310050/2019-7 and 302413/2022-7, Fundação de Amparo à Ciência e Tecnologia de Pernambuco (FACEPE) process number APQ-0987-1.02/21 and Coordination for the Improvement of Higher Level – or Education – Personnel (Capes). Uribe-Opazo would like to acknowledge CNPq process number 306561/2020-4, Brazil.