Academic literature on the topic 'Hierarchical spatial modeling'

Differentiation in the level of socio-economic development of territories is largely manifested in both inter-regional and intra-regional differences in personal income and consumption of goods. In this regard the methods of hierarchical analysis (HLM, Hierarchical Linear Modeling) that make it possible to study variation at several levels taking into account both municipal and regional factors are acquiring special relevance. Along with hierarchical effects, neighborhood effects can be distinguished. This is possible due to the imposition of a spatial adjacency matrix on the data observing spatial interactions within the spatial-hierarchical models (HSAM, Hierarchical Spatial Autoregressive Modeling). The aim of the study is to better understand the relationship between consumption and personal income within a hierarchically structured and spatially oriented economic system. The analysis uses the data from 2319 municipalities (i.e. municipal districts or rayons) and urban districts (okrugs) in 84 constituent entities of the Russian Federation for 2018. It showed that 38.4% of the variation among municipalities in terms of sold foods volume is explained by regional factors. The developed hierarchical (two-level) model revealed the positive impact of the volume of social benefits and taxable personal income in the municipality, and the volume of per capita retail trade at the level of the Russian Federation constituent entities, on the volume of foods sold within municipalities, and substantiate the negative impact of the Gini index increase, as well as highlight the positive spatial effect

Hierarchical Bayesian models (HBM) are powerful tools that can be used for spatiotemporal analysis. The hierarchy feature associated with Bayesian modeling enhances the accuracy and precision of spatiotemporal predictions. This paper leverages the hierarchy of the Bayesian approach using the three models; the Gaussian process (GP), autoregressive (AR), and Gaussian predictive processes (GPP) to predict long-term traffic status in urban settings. These models are applied on two different datasets with missing observation. In terms of modeling sparse datasets, the GPP model outperforms the other models. However, the GPP model is not applicable for modeling data with spatial points close to each other. The AR model outperforms the GP models in terms of temporal forecasting. The GP model is used with different covariance matrices: exponential, Gaussian, spherical, and Matérn to capture the spatial correlation. The exponential covariance yields the best precision in spatial analysis with the Gaussian process, while the Gaussian covariance outperforms the others in temporal forecasting.

As a critical task in intelligent traffic systems, traffic prediction has received a large amount of attention in the past few decades. The early efforts mainly model traffic prediction as the time-series mining problem, in which the spatial dependence has been largely ignored. As the rapid development of deep learning, some attempts have been made in modeling traffic prediction as the spatio-temporal data mining problem in a road network, in which deep learning techniques can be adopted for modeling the spatial and temporal dependencies simultaneously. Despite the success, the spatial and temporal dependencies are only modeled in a regionless network without considering the underlying hierarchical regional structure of the spatial nodes, which is an important structure naturally existing in the real-world road network. Apart from the challenge of modeling the spatial and temporal dependencies like the existing studies, the extra challenge caused by considering the hierarchical regional structure of the road network lies in simultaneously modeling the spatial and temporal dependencies between nodes and regions and the spatial and temporal dependencies between regions. To this end, this article proposes a new Temporal Hierarchical Graph Attention Network (TH-GAT). The main idea lies in augmenting the original road network into a region-augmented network, in which the hierarchical regional structure can be modeled. Based on the region-augmented network, the region-aware spatial dependence model and the region-aware temporal dependence model can be constructed, which are two main components of the proposed TH-GAT model. In addition, in the region-aware spatial dependence model, the graph attention network is adopted, in which the importance of a node to another node, of a node to a region, of a region to a node, and of a region to another region, can be captured automatically by means of the attention coefficients. Extensive experiments are conducted on two real-world traffic datasets, and the results have confirmed the superiority of the proposed TH-GAT model.