# Spatial–Temporal Patterns of Population Aging in Rural China

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials

#### 2.1. Study Area

#### 2.2. Evaluation Index of Rural Population Aging

#### 2.3. Construction of the Indicator System

#### 2.4. Data Sources and Arrangement

## 3. Methods

#### 3.1. Getis–Ord Gi*

#### 3.2. Standard Deviational Ellipse

#### 3.3. Geographical Detector: Influence Factor Analysis of Rural Population Aging

- (1)
- The factor detector quantifies the influences of factors on the q-statistics. In this study, the factor detector identifies which factors are responsible for the RPA. Its formula is:$$q=1-\frac{{{\displaystyle \sum}}_{h=1}^{L}{N}_{h}{\sigma}_{h}{}^{2}}{{N}_{\sigma}{}^{2}}=1-\frac{SSW}{SST}$$
- (2)
- The interaction detector examines whether two independent variables, when taken together, weaken or enhance each another or whether they are independent in developing dependent variables [36]. In this study, the interaction detector examines whether the factors (${x}_{1}$ and ${x}_{2}$) have an interactive effect on RPA. First, the q-statistics of factors ${x}_{1}$ and ${x}_{2}$, in respect of the RPA, were calculated and marked as $q({x}_{1})$ and $q({x}_{2})$. Then, the interactive q-statistics of factors ${x}_{1}$ and ${x}_{2}$ were calculated and marked as $q({x}_{1}\cap {x}_{2})$. The interactive relationship can be classified into five types by comparing the interactive q-statistics of the two factors and the q-statistics of each of the two factors [37]. The five types are described in Table 2.
- (3)
- The ecological detector, which is determined by the F-statistics, is used to compare whether the impacts of the two factors (${x}_{1}$ and ${x}_{2}$) on the dependent variable have a significant difference [38]:$$F=\frac{{N}_{{x}_{1}}\left({N}_{{x}_{2}}-1\right)SS{W}_{{x}_{1}}}{{N}_{{x}_{2}}\left({N}_{{x}_{1}}-1\right)SS{W}_{{x}_{2}}}$$$$SS{W}_{{x}_{1}}={{\displaystyle \sum}}_{h=1}^{{L}_{1}}{N}_{h}{\sigma}_{h}{}^{2},SS{W}_{{x}_{2}}={{\displaystyle \sum}}_{h=2}^{{L}_{2}}{N}_{h}{\sigma}_{h}{}^{2}$$
- (4)
- The risk detector is used to detect whether the spatial–temporal pattern of RPA is remarkably different, whereas the area studied is stratified by a variety of factors. If the result of the two factors is “Y”, it means there are significant differences between the two factors that influence RPA, whereas if the result of the two factors is “N”, it means there is no significant difference. The risk detection is examined using t-statistics:$$t=\frac{{\overline{Y}}_{h=1}-{\overline{Y}}_{h=2}}{{\left[\frac{Var\left({Y}_{h=1}\right)}{{n}_{h}=1}+\frac{Var\left({Y}_{h=2}\right)}{{n}_{h}=2}\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$$

## 4. Results

#### 4.1. Spatial Distributions of Rural Aging in China

#### 4.2. Hot Spots Analysis of Rural Population Aging

#### 4.3. Analysis of Directional Evolution of the RPA

#### 4.4. The Driving Forces of RPA on Geographical Detector

#### 4.4.1. The Analysis of Factor Detector on RPA

#### 4.4.2. The Analysis of Interaction Detector on RPA

#### 4.4.3. Statistical Significance of Differences among Driving Factors

## 5. Discussions

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- United Nations. World Population Prospects 2019: Highlights; Department of Economic and Social Affairs: New York, NY, USA, 2019. [Google Scholar]
- Bloom, D.E.; Boersch-Supan, A.; McGee, P.; Seike, A. Population aging: Facts, challenges, and responses. Benefits Compens. Int.
**2011**, 41, 22. Available online: https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1288/2013/10/PGDA_WP_71.pdf (accessed on 25 March 2022). - China Statistical Yearbook. Available online: http://www.stats.gov.cn/tjsj/ndsj (accessed on 26 March 2022).
- Cousins, M. The sustainability of China’s Urban Employees’ Pension Programme: A case of getting old before getting rich? Int. Soc. Secur. Rev.
**2021**, 74, 59–77. [Google Scholar] [CrossRef] - Xu, X.; Zhao, Y.; Zhang, X.L.; Xia, S.Y. Identifying the impacts of social, economic, and environmental factors on population aging in the Yangtze River Delta using the geographical detector technique. Sustainability
**2018**, 10, 1528. [Google Scholar] [CrossRef] - Wang, S. Spatial patterns and social-economic influential factors of population aging: A global assessment from 1990 to 2010. Soc. Sci. Med.
**2020**, 253, 112963. [Google Scholar] [CrossRef] - Galor, O. The demographic transition: Causes and consequences. Cliometrica
**2012**, 6, 1–28. [Google Scholar] [CrossRef] - Wu, Y.Y.; Song, Y.X.; Yu, T.T. Spatial differences in China’s population aging and influencing factors: The perspectives of spatial dependence and spatial heterogeneity. Sustainability
**2019**, 11, 5959. [Google Scholar] [CrossRef] - Statistical Table of Administrative Divisions of the People’s Republic of China. Available online: http://xzqh.mca.gov.cn/statistics/2019.html (accessed on 8 October 2022).
- Liu, M.G. Atlas of Physical Geography of China, 3rd ed.; Sinomap Press: Beijing, China, 2010; p. 247. [Google Scholar]
- United Nations. The Aging of Populations and Its Economic and Social Implications; Population Studies No. 26; Department of Economic and Social Affairs; Sales No.E.56.XIII.6; New York, NY, USA, 1956. [Google Scholar]
- Wang, L.C.; Wu, R.W.; Li, W. Spatial-temporal patterns of population aging on China’s urban agglomerations. Acta Geogr. Sin.
**2017**, 72, 1001–1016. (In Chinese) [Google Scholar] [CrossRef] - Raymer, J.; Willekens, F.; Rogers, A. Spatial demography: A unifying core and agenda for further research. Popul. Space Place
**2019**, 25, e2179. [Google Scholar] [CrossRef] - World Health Organization. Global Health and Aging, National Institute on Aging; National Institutes of Health: New York, NY, USA, 2011. [Google Scholar]
- Wilmoth, J.R. The future of human longevity: A demographer’s perspective. Science
**1998**, 280, 395–397. [Google Scholar] [CrossRef] - Yang, M.Q.; Rosenberg, M.W.; Li, J. Spatial variability of health inequalities of older people in China and related health factors. Int. J. Environ. Res. Public Health
**2020**, 17, 1739. [Google Scholar] [CrossRef] - Wu, J.X.; He, L.Y. Urban–rural gap and poverty traps in China: A prefecture level analysis. Appl. Econ.
**2018**, 50, 3300–3314. [Google Scholar] [CrossRef] - State Council Census Office. Tabulation on the 2000 Population Census of the People’s Republic of China by County; China Statistics Press: Beijing, China, 2001.
- State Council Census Office. Tabulation on the 2010 Population Census of the People’s Republic of China by County; China Statistics Press: Beijing, China, 2011.
- Tabulation on the 2020 Population Census of the People’s Republic of China by County. Available online: https://tjgb.hongheiku.com/%e4%b8%ad%e5%9b%bd (accessed on 7 December 2021).
- Ord, J.K.; Getis, A. Local spatial autocorrelation statistics: Distributional issues and an application. Geogr. Anal.
**1995**, 27, 286–306. [Google Scholar] [CrossRef] - Songchitruksa, P.; Zeng, X.S. Getis–Ord spatial statistics to identify hot spots by using incident management data. Transp. Res. Rec.
**2010**, 2165, 42–51. [Google Scholar] [CrossRef] - Lefever, D.W. Measuring geographic concentration by means of the standard deviational ellipse. Am. J. Sociol.
**1926**, 32, 88–94. [Google Scholar] [CrossRef] - Xia, X.X.; Li, H.C.; Kuang, X.J.; Strauss, J. Spatial–Temporal Features of Coordination Relationship between Regional Urbanization and Rail Transit—A Case Study of Beijing. Int. J. Environ. Res. Public Health
**2022**, 19, 212. [Google Scholar] [CrossRef] - Yuill, R.S. The standard deviational ellipse; an updated tool for spatial description. Geogr. Ann. Ser. B Hum. Geogr.
**1971**, 53, 28–39. [Google Scholar] [CrossRef] - Moore, T.W.; McGuire, M.P. Using the standard deviational ellipse to document changes to the spatial dispersion of seasonal tornado activity in the United States. NPJ Clim. Atmos. Sci.
**2019**, 2, 1–8. [Google Scholar] [CrossRef] - Shi, J.L.; Gao, X.; Xue, S.Y.; Li, F.Q.; Nie, Q.F.; Lv, Y.F.; Wang, J.B.; Xu, T.T.; Du, G.X.; Li, G. Spatio-temporal evolution and influencing mechanism of the COVID-19 epidemic in Shandong province, China. Sci. Rep.
**2021**, 11, 1–16. [Google Scholar] [CrossRef] - Rogerson, P.A. Historical change in the large-scale population distribution of the United States. Appl. Geogr.
**2021**, 136, 102563. [Google Scholar] [CrossRef] - Gong, J.X. Clarifying the standard deviational ellipse. Geogr. Anal.
**2002**, 34, 155–167. [Google Scholar] [CrossRef] - Cao, F.; Ge, Y.; Wang, J.F. Optimal discretization for geographical detectors-based risk assessment. GIScience Remote Sens.
**2013**, 50, 78–92. [Google Scholar] [CrossRef] - Fan, Z.X.; Duan, J.; Lu, Y.; Zou, W.T.; Lan, W.L. A geographical detector study on factors influencing urban park use in Nanjing, China. Urban For. Urban Green.
**2021**, 59, 126996. [Google Scholar] [CrossRef] - Wang, J.F.; Xu, C.D.; Tong, S.L.; Chen, H.Y.; Yang, W.Z. Spatial dynamic patterns of hand-foot-mouth disease in the Peopleâ€™ s Republic of China. Geospat. Health
**2013**, 7, 381–390. [Google Scholar] [CrossRef] [PubMed] - Zhan, D.S.; Kwan, M.P.; Zhang, W.Z.; Fan, J.; Yu, J.H.; Dang, Y.X. Assessment and determinants of satisfaction with urban livability in China. Cities
**2018**, 79, 92–101. [Google Scholar] [CrossRef] - Zhao, R.; Zhan, L.P.; Yao, M.X.; Yang, L.C. A geographically weighted regression model augmented by Geodetector analysis and principal component analysis for the spatial distribution of PM2.5. Sustain. Cities Soc.
**2020**, 56, 102106. [Google Scholar] [CrossRef] - Zhou, Y.; Li, X.H.; Liu, Y.S. Land use change and driving factors in rural China during the period 1995–2015. Land Use Policy
**2020**, 99, 105048. [Google Scholar] [CrossRef] - Wang, J.F.; Li, X.H.; Christakos, G.; Liao, Y.L.; Zhang, T.; Gu, X.; Zheng, X.Y. Geographical detectors-based health risk assessment and its application in the neural tube defects study of the Heshun Region, China. Int. J. Geogr. Inf. Sci.
**2010**, 24, 107–127. [Google Scholar] [CrossRef] - Wang, J.F.; Hu, Y. Environmental health risk detection with GeogDetector. Environ. Model. Softw.
**2012**, 33, 114–115. [Google Scholar] [CrossRef] - Yue, H.; Hu, T. Geographical Detector-Based Spatial Modeling of the COVID-19 Mortality Rate in the Continental United States. Int. J. Environ. Res. Public Health
**2021**, 18, 6832. [Google Scholar] [CrossRef] - Hu, Y.; Wang, J.F.; Li, X.H.; Ren, D.; Zhu, J. Geographical detector-based risk assessment of the under-five mortality in the 2008 Wenchuan earthquake, China. PLoS ONE
**2011**, 6, e21427. [Google Scholar] [CrossRef] - Wu, L.X.; Huang, Z.Y.; Pan, Z.H. The spatiality and driving forces of population ageing in China. PLoS ONE
**2021**, 16, e0243559. [Google Scholar] [CrossRef] - Su, B.Z.; Li, Y.H.; Zheng, X.D. Who are to support the aged in rural China? The study of people’s willingness to purchase socialized care service and its influencing factors. J. Rural. Stud.
**2020**, 93, 496–503. [Google Scholar] [CrossRef]

**Figure 2.**Spatial distribution profiles of China’s rural population aging ratio in 2000 (

**a**), 2010 (

**b**), and 2020 (

**c**).

**Figure 3.**Spatial clustering (hot and cold spots) analysis of China’s rural population aging in 2000 (

**a**), 2010 (

**b**), and 2020 (

**c**).

Variable Systems | Variables (Abbreviation) | Descriptions |
---|---|---|

Natural and mechanical demographic characteristics | Total population (TPOP) | The total population in each county |

The proportion of 55 to 64 years old (P55-64) ten years ago | P55-64 represents the base of aged people | |

Fertility rate (FER) | The proportion of births in the total population | |

Longevity rate (LGV) | The proportion of the population aged 80 and above in the total population | |

Migration rate (MIG) | Hukou^{1-}registered population in other places/Hukou-registered population in local places | |

Socioeconomic characteristics | Per capita GDP (PGDP) | The per capita GDP of each county |

Urbanization rate (UBZ) | The proportion of nonagricultural Hukou in total population | |

Healthcare accessibility characteristics | Number of hospitals (HOS) | The number of hospitals in each county |

Number of beds (BED) | The number of beds in each county | |

Educational characteristics | Per capita years of education (PEDU) | Refers to the average years of education of the population aged 6 and over. A college degree or above is calculated as 16 years, 12 years for high school, 9 years for junior high school, 6 years for primary school, and 0 years for illiteracy |

Illiteracy rate (ILT) | The proportion of illiterate people aged 15 and over in the total population |

^{1}means the household registration system in China, which includes nonagricultural Hukou and agricultural Hukou.

Title 1 | Description |
---|---|

Weakened, nonlinear | $q({x}_{1}\cap {x}_{2})<Min\left(q({x}_{1}\right),q({x}_{2}))$ |

Weakened, univariate | $Min\left(q({x}_{1}\right),q({x}_{2}))q({x}_{1}\cap {x}_{2})Max\left(q({x}_{1}\right),q({x}_{2}))$ |

Enhanced, nonlinear | $q({x}_{1}\cap {x}_{2})>q({x}_{1})+q({x}_{2})$ |

Enhanced, bivariate | $q({x}_{1}\cap {x}_{2})<Max\left(q({x}_{1}\right),q({x}_{2}))$ |

Independent | $q({x}_{1}\cap {x}_{2})=q({x}_{1})+q({x}_{2})$ |

Year | Center X | Center Y | $\mathit{t}\mathit{a}{\mathit{n}}_{\mathit{\theta}}/\xb0$ | $\mathbf{Long}\mathbf{Axis}\left({\mathit{\alpha}}_{\mathit{x}}\right)/\mathbf{km}$ | $\mathbf{Short}\mathbf{Axis}\left({\mathit{\alpha}}_{\mathit{y}}\right)/\mathbf{km}$ |
---|---|---|---|---|---|

2000 | $32.91\xb0\mathrm{N}$ | $112.71\xb0\mathrm{E}$ | $69.5\xb0$ | 12,776.79 | 8439.85 |

2010 | $33.12\xb0\mathrm{N}$ | $112.61\xb0\mathrm{E}$ | $68.8\xb0$ | 12,962.98 | 8589.18 |

2020 | $33.59\xb0\mathrm{E}$ | $113.19\xb0\mathrm{E}$ | $63.6\xb0$ | 12,839.65 | 8140.22 |

Factors | Central | Eastern | Northern | Northeast | Northwest | Southern | Southwest |
---|---|---|---|---|---|---|---|

TPOP | 0.057 | 0.467 | 0.125 | 0.516 | 0.087 | 0.01 | 0.113 |

P55-64 | 0.052 | 0.672 | 0.273 | 0.722 | 0.138 | 0.066 | 0.023 |

FER | 0.082 | 0.516 | 0.104 | 0.629 | 0.09 | 0.131 | 0.177 |

LGV | 0.383 | 0.427 | 0.619 | 0.814 | 0.369 | 0.081 | 0.707 |

MIG | 0.175 | 0.651 | 0.364 | 0.486 | 0.118 | 0.048 | 0.159 |

PGDP | 0.165 | 0.711 | 0.065 | 0.644 | 0.157 | 0.078 | 0.127 |

UBZ | 0.323 | 0.893 | 0.372 | 0.798 | 0.153 | 0.104 | 0.351 |

HOS | 0.055 | 0.039 | 0.104 | 0.123 | 0.025 | 0.141 | 0.435 |

BED | 0.015 | 0.054 | 0.088 | 0.229 | 0.117 | 0.146 | 0.368 |

PEDU | 0.04 | 0.065 | 0.167 | 0.621 | 0.105 | 0.125 | 0.458 |

ILT | 0.028 | 0.124 | 0.205 | 0.242 | 0.094 | 0.089 | 0.388 |

**Table 5.**The interaction detector analysis and statistically significant differences of the driving factors on RPA.

Variables | Demographic | Socioeconomic | Healthcare | Educational | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

TPOP | P55-64 | FER | LGV | MIG | PGDP | UBZ | HOS | BED | PEDU | ILT | |

TPOP | |||||||||||

P55-64 | 0.61 (EB, Y) | ||||||||||

FER | 0.25 (EB, Y) | 0.61 (EB, Y) | |||||||||

LGV | 0.74 (EB, Y) | 0.82 (EB, Y) | 0.74 (EB, Y) | ||||||||

MIG | 0.20 (EB, Y) | 0.61 (EB, Y) | 0.18 (EN, Y) | 0.74 (EB, Y) | |||||||

PGDP | 0.19 (EN, Y) | 0.62 (EB, Y) | 0.14 (EB, Y) | 0.73 (EB, Y) | 0.11 (EN, Y) | ||||||

UBZ | 0.24 (EB, Y) | 0.62 (EB, Y) | 0.20 (EB, N) | 0.73 (EB, Y) | 0.15 (EN, Y) | 0.14 (EN, Y) | |||||

HOS | 0.25 (EB, Y) | 0.62 (EB, Y) | 0.30 (EN, Y) | 0.72 (EB, Y) | 0.24 (EB, Y) | 0.24 (EN, Y) | 0.26 (EB, Y) | ||||

BED | 0.20 (EB, N) | 0.61 (EB, Y) | 0.26 (EB, Y) | 0.73 (EB, Y) | 0.21 (EB, Y) | 0.21 (EN, Y) | 0.26 (EB, Y) | 0.25 (EB, Y) | |||

PEDU | 0.24 (EB, N) | 0.64 (EB, Y) | 0.26 (EB, Y) | 0.74 (EB, Y) | 0.20 (EB, Y) | 0.2 (EN, Y) | 0.22 (EB, Y) | 0.28 (EB, Y) | 0.25 (EB, N) | ||

ILT | 0.22 (EB, Y) | 0.64 (EB, Y) | 0.22 (EB, Y) | 0.74 (EB, Y) | 0.19 (EN, Y) | 0.19 (EN, Y) | 0.23 (EB, Y) | 0.27 (EB, Y) | 0.24 (EB, Y) | 0.20 (EB, Y) |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chen, C.; Li, J.; Huang, J. Spatial–Temporal Patterns of Population Aging in Rural China. *Int. J. Environ. Res. Public Health* **2022**, *19*, 15631.
https://doi.org/10.3390/ijerph192315631

**AMA Style**

Chen C, Li J, Huang J. Spatial–Temporal Patterns of Population Aging in Rural China. *International Journal of Environmental Research and Public Health*. 2022; 19(23):15631.
https://doi.org/10.3390/ijerph192315631

**Chicago/Turabian Style**

Chen, Chan, Jie Li, and Jian Huang. 2022. "Spatial–Temporal Patterns of Population Aging in Rural China" *International Journal of Environmental Research and Public Health* 19, no. 23: 15631.
https://doi.org/10.3390/ijerph192315631