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Is a matrix exponential specification suitable for the modeling of spatial correlation structures?

ABSTRACT: This paper investigates the adequacy of the matrix exponential spatial specifications (MESS) as an alternative to the widely used spatial autoregressive models (SAR). To provide as complete a picture as possible, we extend the analysis to all the main spatial models governed by matrix exponentials comparing them with their spatial autoregressive counterparts. We propose a new implementation of Bayesian parameter estimation for the MESS model with vague prior distributions, which is shown to be precise and computationally efficient. Our implementations also account for spatially lagged regressors. We further allow for location-specific heterogeneity, which we model by including spatial splines. We conclude by comparing the performances of the different model specifications in applications to a real data set and by running simulations. Both the applications and the simulations suggest that the spatial splines are a flexible and efficient way to account for spatial heterogeneities governed by unknown mechanisms.

SUBMITTER: Strauß ME

PROVIDER: S-EPMC5826581 | biostudies-literature | 2017 May

REPOSITORIES: biostudies-literature

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Is a matrix exponential specification suitable for the modeling of spatial correlation structures?

Strauß Magdalena E ME Mezzetti Maura M Leorato Samantha S

Spatial statistics 20170427

This paper investigates the adequacy of the matrix exponential spatial specifications (MESS) as an alternative to the widely used spatial autoregressive models (SAR). To provide as complete a picture as possible, we extend the analysis to all the main spatial models governed by matrix exponentials comparing them with their spatial autoregressive counterparts. We propose a new implementation of Bayesian parameter estimation for the MESS model with vague prior distributions, which is shown to be p ...[more]

PMID: 29492375

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Project description:The formation of many sources of pollution in a short period of time is due to mountain soil erosion by water. One of the major mechanisms decisive in the intensification of such erosion is the loosening of soil material on the slope. Water quality studies show the impact of diversified spatial management and allow making the right decisions in environmental management in mountain areas with high variability of use and land cover. The research undertaken as part of the paper was carried out in order to determine the dependency between total suspended solids (TSS) and the physicochemical parameters of surface waters and the amount of soil losses in the use structure within the mountain catchment. The paper focused on the frequency of phenomena in time and the possibility of stopping the surface runoff on the slope and on the soil's susceptibility to water erosion. The dependencies between multipoint sampling and the concentration of material washed off the slope due to precipitation were verified with a multivariate analysis. Sampling took place in hydrometric sections, and during small floods, in the waterbed cross section. Research shows that such sampling is the basis for the calculation of the transported load, reflecting the average variation in concentration. The variation in the volume of the load from the individual parts of the catchment was assessed by the spatial autoregressive model. It was found that the use of river basin areas affects water chemistry. Water reservoirs are an important ecological barrier for the migration of nitrate nitrogen (N-NO3) and phosphate phosphorus (P-PO4), which is marked by changes in the growing season. Water along the sections of the river near the quarry with a high degree of sodding showed good quality condition. Despite significant differences between measurement sampling sites, high total dissolved solid (TDS) values were found in communities adjacent to forests and meadows. However, the highest electrical conductivity (EC) and TSS concentrations were found in the interface with cultivated areas. Biogenic indices showed variation depending on the way the adjacent areas were used. GIS linked spatial variables with the formation of water pollution. The analysis of spatial autoregression pointed to the impact of arable land. Moreover, the analysis of spatial autoregression with the MESS function designated a connection between agricultural land use and nitrite nitrogen (N-NO2), EC, TSS, and dissolved oxygen (DO). Graphical abstract ᅟ.

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Is a matrix exponential specification suitable for the modeling of spatial correlation structures?

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Is a matrix exponential specification suitable for the modeling of spatial correlation structures?

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