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16 pages, 326 KiB

Open AccessArticle

A Marginal Maximum Likelihood Approach for Hierarchical Simultaneous Autoregressive Models with Missing Data

by Anjana Wijayawardhana, David Gunawan and Thomas Suesse

Mathematics 2024, 12(23), 3870; https://doi.org/10.3390/math12233870 - 9 Dec 2024

Cited by 1 | Viewed by 808

Efficient estimation methods for simultaneous autoregressive (SAR) models with missing data in the response variable have been well explored in the literature. A common practice is introducing measurement error into SAR models to separate the noise component from the spatial process. However, prior studies have not considered incorporating measurement error into SAR models with missing data. Maximum likelihood estimation for such models, especially with large datasets, poses significant computational challenges. This paper proposes an efficient likelihood-based estimation method, the marginal maximum likelihood (ML), for estimating SAR models on large datasets with measurement errors and a high percentage of missing data in the response variable. The spatial autoregressive model (SAM) and the spatial error model (SEM), two popular SAR model types, are considered. The missing data mechanism is assumed to follow a missing-at-random (MAR) pattern. We propose a fast method for marginal ML estimation with a computational complexity of

$O (n^{3 / 2})$ , where n is the total number of observations. This complexity applies when the spatial weight matrix is constructed based on a local neighbourhood structure. The effectiveness of the proposed methods is demonstrated through simulations and real-world data applications. Full article

(This article belongs to the Section D1: Probability and Statistics)

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21 pages, 5848 KiB

Open AccessArticle

What Factors Revitalize the Street Vitality of Old Cities? A Case Study in Nanjing, China

by Yan Zheng, Ruhai Ye, Xiaojun Hong, Yiming Tao and Zherui Li

ISPRS Int. J. Geo-Inf. 2024, 13(8), 282; https://doi.org/10.3390/ijgi13080282 - 12 Aug 2024

Cited by 2 | Viewed by 1622

Abstract

Urban street vitality has been a perennial focus within the domain of urban planning. This study examined spatial patterns of street vitality in the old city of Nanjing during working days and weekends using real-time user datasets (RTUDs). A spatial autoregressive model (SAM) and a multiscale geographically weighted regression (MGWR) model were employed to quantitatively assess the impact of various factors on street vitality and their spatial heterogeneity. This study revealed the following: (1) the distribution of street vitality in the old city of Nanjing exhibited a structure centered around Xinjiekou, with greater regularity and predictability in street vitality on working days than on weekends; (2) eight variables, such as traffic location, road density, and functional density, are positively associated with street vitality, whereas the green view index is negatively associated with street vitality, and commercial location benefits street vitality at weekends but detracts from street vitality on working days; and (3) the influence of variables such as traffic location and functional density on street vitality is contingent on their spatial position. Based on these results, this study provides new strategies to enhance the street vitality of old cities. Full article

(This article belongs to the Topic Spatial Decision Support Systems for Urban Sustainability)

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13 pages, 1774 KiB

Open AccessArticle

Examining Vulnerability Factors to Natural Disasters with a Spatial Autoregressive Model: The Case of South Korea

by Seunghoo Jeong and D. K. Yoon

Sustainability 2018, 10(5), 1651; https://doi.org/10.3390/su10051651 - 20 May 2018

Cited by 31 | Viewed by 6278

Abstract

Socially and economically marginalized people and environmentally vulnerable areas are disproportionately affected by natural hazards. Identifying populations and places vulnerable to disasters is important for disaster management, and crucial for mitigating their economic consequences. From the fields of geography, emergency management, and urban planning, several approaches and methodologies have been used to identify significant vulnerability factors affecting the incidence and impact of disasters. This study performs a regression analysis to examine several factors associated with disaster damage in 230 local communities in South Korea, using ten vulnerability indicators for social, economic, and environmental aspects, and a single indicator for disaster characteristics. A Lagrange Multiplier diagnostic test-based spatial autoregressive model (SAM) was applied to assess the potential spatial autocorrelation in the ordinary least squares (OLS) residuals. This study compared the OLS regression results with those of a spatial autoregressive model, for both presence of spatial autocorrelation, and model performance. The conclusion of this study is that Korean communities with a higher vulnerability to disasters, as a result of their socioeconomic and environmental characteristics, are more likely to experience economic losses from natural disasters. Full article

(This article belongs to the Section Sustainable Urban and Rural Development)

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