Spatial feature analysis of rural basic public service supply based on TOPSIS model and Data aggregation algorithm

Abstract

The provision of basic public services in rural areas is a necessary condition for promoting farmers, agriculture, and rural development, and has important economic effects. The supply of basic public services in rural areas has an impact on agricultural growth, rural poverty reduction, and farmers’ production and investment, and ultimately directly or indirectly affect farmers’ income and consumption. In order to effectively improve the effectiveness of providing basic public services in rural areas, this study takes rural basic public services as the research object, and analyzes the economic and geographic perspectives, models, and algorithms of supply effectiveness through a literature review. It was found that the research area level needs to be deepened, and the shortcomings of traditional models and algorithms were also found. This article will make full use of the TOPSIS model’s methodological advantages in comprehensive ranking, combine the entropy method with the TOPSIS model, and sort the evaluation objects by approaching the optimal solution, so as to more objectively evaluate the rural basic public service supply in the sample counties. Based on the data aggregation algorithm, with the help of spatial analysis methods, Gini coefficient, and Theil index to further study the spatial distribution characteristics of supply. The research shows that the method has good performance and can be used as a reference for the subsequent related research rural basic services theory.

Keywords

TOPSIS model rural basic public services spatial analysis

1 Introduction

Since the reform and opening up, China’s economic development has achieved world-renowned achievements. Among them, agriculture has always shouldered the heavy responsibility of stabilizing the national economic foundation. However, the gap between urban and rural development has kept farmers’ livelihood improvements away from economic growth for a long time. The sharing of the fruits of economic development in different places is concentrated in the inequality of basic public services in urban and rural areas. At present, basic public services in rural areas such as education, medical care, pensions, and residence are the most concerned, most direct, and most relevant manifestations of the interests of farmers, and are the limiting factors for farmers’ growing needs for a better life. Basic public services are a limiting factor for farmers’ growing needs for a better life, and they are also a prominent shortcoming of building a well-off society in an all-round way. The provision of basic public services in rural areas can bring more development possibilities for the rural economy, improve rural living environment and living conditions, help the rural poor to achieve poverty alleviation, strengthen the collective economy, and reduce the urban-rural gap. The report of the 19th National Congress of the Communist Party of China puts forward the top-level design that adheres to the priority development of agriculture and rural areas. The priority of public service arrangements is one of them. Complementing the shortcomings of basic public services in rural areas is an inevitable choice to achieve the development results shared by all. Therefore, it is necessary to benchmark the goal of achieving a comprehensive well-off in 2020 and the equalization of basic public services in 2035, deploying in accordance with the arrangements for the rural revitalization strategy, establishing a scientific rural basic public service indicator system, and clarifying the supply of basic rural public services. On this basis, we should analyze the characteristics of spatial distribution, grasp the allocation of supply resources, and provide theoretical support and practical basis for the equalization of basic public services in urban and rural areas.

2 Related work

From the existing research, many scholars have researched the supply of basic public services in rural areas from different angles and using different methods. Most of the research has focused on investment [1, 2], supply efficiency [3, 4] and evaluation of farmers [5, 6]. Among them, some scholars have established an evaluation index system for the supply level, collected data from statistical yearbooks to measure the supply level, and evaluated the supply of basic public services in rural areas. Most of them are based on objective evaluation methods such as entropy and factor analysis. From the perspective of economic geography, some scholars study the supply level from the national and provincial levels [7 –9], and some scholars study the supply level from the city level and below [10 –12]. Existing studies have shown that regional imbalances in the supply of basic rural public services in China are severe, and that there are large differences in the level of supply of different types of rural basic public services in different regions. However, the existing studies are mainly aimed at large-scale regional analysis of provincial administrative units. The indicator system constructed is not sufficient to reflect the focus of attention under the rural revitalization strategy, and it also ignores the level of rural basic public service supply within the provincial administrative unit. regional difference. In the study, few scholars have analyzed the regional differences and spatial analysis of the supply level at the county level, and few have comprehensively analyzed the supply level of basic rural public services based on agricultural census data. At the same time, the government power allocation system combining economic decentralization and political centralization determines the core position of county-level governments in the provision of basic public services in rural areas, and fully confirms the necessity and importance of researching supply issues at the county level. In related studies abroad, many scholars analyze the differences in the level of basic public service supply in the study area from different dimensions or perspectives, and use spatial analysis methods and tools to explore the characteristics of spatial and temporal differentiation [13 –15].

In view of this, this article combines the realistic background of the rural revitalization strategy, uses the data of the third national agricultural census of Heilongjiang Province, and designs an evaluation system for the supply level of basic public services in rural areas. Based on the entropy method and the TOPSIS model, the basic public service supply level in rural areas of Heilongjiang Province was evaluated from the scale of county-level administrative units. Based on the data aggregation algorithm, with the help of spatial autocorrelation, Gini coefficient, and Theil index and other analysis methods to further study the distribution characteristics of supply, in order to comprehensively evaluate the supply level of basic public services in rural Heilongjiang Province, and find shortcomings in supply. In addition, it provides decision-making references to promote the rational allocation of supply resources and provides a basis for government policy formulation.

3 Evaluation system and research method

3.1 Construction of indicator system

There is overlap among scholars on the definition and scope of basic rural public services in China, but no consensus conclusion has been reached. Most scholars agree that the connotation of rural basic public services is relatively broad and has many classifications, and its scope often depends on the needs of farmers, and the needs of farmers change with the changes in the rural economic and social environment. In recent years, most researches have been based on the definition of the concepts in The 12th Five-Year Plan of the National Basic Public Service System or the basic public service list in The 13th Five-Year Plan to Promote the Equalization of Basic Public Services, combining different research purposes to finalize the evaluation system for the supply of basic rural public services. Based on the previous research results, this article refers to the relevant content in The 13th Five-Year Plan to Promote the Equalization of Basic Public Services and The Rural Strategic Planning (2018-2022), and follow the systematic and typical principles of index selection. Typical, and taking into account the availability and comparability of the data, it also innovatively added rural human settlements environmental evaluation indicators, and finally established an evaluation system of basic public service supply levels in rural areas that includes 38 specific indicators in 11 aspects. The supply indicator system is shown in Table 1.

Table 1
Rural basic public service supply indicator system

First-level indicators Secondary-level indicators

Rural transportation logistics facilities Proportion of towns with railway stations

Proportion of towns with highway entrances and exits

Proportion of villages whose main road pavement is cement pavement

Proportion of villages with e-commerce distribution sites

Farmland water conservancy infrastructure Area of arable land with sprinkler, drip and infiltration irrigation facilities at the end of the year

Number of mechanical and electrical wells that can be used normally

Number of drainage and irrigation stations

Ponds and reservoirs for irrigation

Rural drinking water Proportion of farmers drinking purified tap water

Proportion of farmers drinking unprotected well water and spring water

Rural modern energy Proportion of villages with natural gas

Proportion of farmers whose main living energy is firewood

Proportion of farmers whose main living energy is solar energy

Rural informatization Proportion of villages connected to broadband Internet

Proportion of villages with cable TV

Rural basic education Proportion of townships with primary schools

The number of kindergartens and nursery schools

Primary school enrollment

Proportion of villages with kindergartens and nurseries

Healthy country Proportion of towns with medical institutions

Proportion of townships with licensed (assistant) physicians

Proportion of villages with health rooms

Proportion of villages with licensed (assistant) physicians

Rural social security and pension services Proportion of townships with social welfare adoption units

Number of urban and rural residents participating in basic endowment insurance

Number of people participating in basic medical insurance in urban and rural areas

Minimum number of people living in urban and rural areas

Townships with homes for the elderly set up by this level of government

Rural housing security Proportion of villages where domestic garbage is concentrated or partially processed

Proportion of villages with concentrated or partially concentrated sewage treatment

Proportion of villages that completed or partially completed toilet modification

Proportion of farmers with flush toilets

Proportion of farmers with sanitary toilets

Rural housing security Proportion of farmers owning their own housing

Proportion of rural households with bamboo and grass adobe structure

Rural public culture and sports Proportion of towns with libraries and cultural stations

Proportion of villages with sports facilities

Proportion of villages with peasant amateur cultural organizations

First-level indicators	Secondary-level indicators
Rural transportation logistics facilities	Proportion of towns with railway stations
	Proportion of towns with highway entrances and exits
	Proportion of villages whose main road pavement is cement pavement
	Proportion of villages with e-commerce distribution sites
Farmland water conservancy infrastructure	Area of arable land with sprinkler, drip and infiltration irrigation facilities at the end of the year
	Number of mechanical and electrical wells that can be used normally
	Number of drainage and irrigation stations
	Ponds and reservoirs for irrigation
Rural drinking water	Proportion of farmers drinking purified tap water
	Proportion of farmers drinking unprotected well water and spring water
Rural modern energy	Proportion of villages with natural gas
	Proportion of farmers whose main living energy is firewood
	Proportion of farmers whose main living energy is solar energy
Rural informatization	Proportion of villages connected to broadband Internet
	Proportion of villages with cable TV
Rural basic education	Proportion of townships with primary schools
	The number of kindergartens and nursery schools
	Primary school enrollment
	Proportion of villages with kindergartens and nurseries
Healthy country	Proportion of towns with medical institutions
	Proportion of townships with licensed (assistant) physicians
	Proportion of villages with health rooms
	Proportion of villages with licensed (assistant) physicians
Rural social security and pension services	Proportion of townships with social welfare adoption units
	Number of urban and rural residents participating in basic endowment insurance
	Number of people participating in basic medical insurance in urban and rural areas
	Minimum number of people living in urban and rural areas
	Townships with homes for the elderly set up by this level of government
Rural housing security	Proportion of villages where domestic garbage is concentrated or partially processed
	Proportion of villages with concentrated or partially concentrated sewage treatment
	Proportion of villages that completed or partially completed toilet modification
	Proportion of farmers with flush toilets
	Proportion of farmers with sanitary toilets
Rural housing security	Proportion of farmers owning their own housing
	Proportion of rural households with bamboo and grass adobe structure
Rural public culture and sports	Proportion of towns with libraries and cultural stations
	Proportion of villages with sports facilities
	Proportion of villages with peasant amateur cultural organizations

3.2 TOPSIS model

The TOPSIS model ranks the evaluation objects by approaching the optimal solution. It has method advantages in comprehensive ranking and is widely used in multi-objective evaluation. In this paper, the TOPSIS model and entropy method are combined to measure the level of rural basic public service supply in the sample counties. The most critical issue in the evaluation of the index system is the determination of the index weight. There are two types of methods for determining the weight, the subjective weighting method and the objective weighting method. The subjective weighting method determines the weight of each indicator by scoring many experts. However, the evaluation of the relative importance of many indicators among experts is prone to large differences. The influence of human factors will increase subjective errors and affect the objectivity of the evaluation results. The objective weighting method is to determine the weight through the mutual relationship between the indicators in the indicator system, which can fully avoid the evaluation errors caused by various human factors, and the accuracy is relatively high. With reference to previous research, this article uses the entropy method in the objective weighting method to determine the weight of each index in the evaluation system. The entropy method determines the weight according to the influence of the relative changes of the indicators in the indicator system on the overall system. The indicators with relatively large changes have a larger weight. This method is widely used in various fields. The specific calculation method and steps are as follows:

The initial evaluation data matrix formed by n indicators in m areas of the study area is: $X = {x_{ij}}_{m * n} 0 ⩽ i ⩽ m, 0 ⩽ j ⩽ n)$

Standardize the indicator data to eliminate the dimensional order of influence of each indicator: $Positive index x_{ij}^{'} = \frac{x_{j} - x_{\min}}{x_{\max} - x_{\min}},$ $Negative indicator x_{ij}^{'} = \frac{x_{\max} - x_{j}}{x_{\max} - x_{\min}}$

Among them, x_j is the j-th index value, x_max is the maximum of the j-th index value, and x_min is the minimum of the j-th index value.

Calculate the proportion of the index value of the i-th area under the j-th index: y_ij: $y_{ij} = \frac{x_{ij}^{'}}{\sum_{i = 1}^{m} x_{ij}^{'}}$

Calculate the information entropy of the j-th index: $e_{j} = - K \sum_{i = 1}^{m} y_{ij} ln (y_{ij}), K = \frac{1}{ln (m)}$

Among them, K = 1/ln(m), and K is a constant.

Calculate the coefficient of variance for the j-th index: $d_{j} = 1 - e_{j}$

Calculate the weight of the j-th indicator: $w_{j} = \frac{d_{j}}{\sum_{i = 1}^{m} d_{j}}$

Calculate the evaluation index weighting matrix: $R = {r_{ij}}_{m * n} 0 ⩽ i ⩽ m, 0 ⩽ j ⩽ n$

Among them, r_ij = w_ij*y_ij

Determine the positive ideal S_j⁺ and negative ideal S_j^- of each indicator: $\begin{matrix} S_{j}^{+} = max (r_{1 j}, r_{2 j}, \cdot \cdot \cdot, r_{mj}), \\ S_{j}^{-} = min (r_{1 j}, r_{2 j}, \cdot \cdot \cdot, r_{mj}) \end{matrix}$

Calculate the Euclidean distances D_j⁺ and D_j^- of the evaluation object to the positive ideal S_j⁺and the negative ideal S_j^-: $D_{i}^{+} = \sqrt{\sum_{j = 1}^{n} {(S_{j}^{+} - r_{ij})}^{2}}$ $D_{i}^{-} = \sqrt{\sum_{j = 1}^{n} {(S_{j}^{-} - r_{ij})}^{2}}$

Calculate the relative closeness C_i between the evaluation object and the optimal solution: $C_{i} = \frac{D_{i}^{-}}{D_{i}^{+} + D_{i}^{-}}$

Among them, 0 ≦C_i ≦ 1, and a larger C_i indicates that the evaluation target is closer to the optimal evaluation level.

3.3 Data aggregation algorithm and exploratory spatial data analysis

Traditional statistical analysis methods often ignore the spatial dependence of the spatial data attribute values. With the rapid development of data algorithms, spatial data has received widespread attention. To analyze the characteristics of data from a spatial perspective, the core is to measure the degree of spatial correlation or dependence between things or phenomena. Based on the data aggregation algorithm, this paper studies the spatial correlation characteristics of basic public service supply level in rural areas of Heilongjiang Province.

Measure the spatial correlation of the study area as a whole. The specific calculation formula is as follows: $I = \frac{\sum_{i = 1}^{n} \sum_{j \neq i}^{n} w_{ij} (x_{i} - \bar{x}) (x_{j} - \bar{x})}{s^{2} \sum_{i = 1}^{n} \sum_{j = 1}^{n} w_{ij}}$ $\bar{x} = \frac{1}{n} \sum_{i = 1}^{n} x_{i}, s^{2} = \frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2}$

Among them, n is the total number of study areas; x_i and x_j are the basic public service supply levels in rural area i and area j, respectively; w_ij is the adjacent space weight matrix of area i and area j. The value of I ranges from -1 to+1, and I > 0 indicates positive spatial correlation, that is, as the spatial distribution position (distance) gathers, the correlation becomes more significant, and the larger the value, the more obvious the spatial correlation. I < 0 indicates spatial negative correlation, that is, as the spatial distribution position is discrete, the correlation becomes significant, and the smaller the value, the larger the spatial difference. When I = 0, the spatial distribution is random.

Analysis of the spatial correlation indicators between each area and the surrounding area can determine the type of spatial aggregation of the research object. An I value is calculated for each region. For area i, the specific calculation formula is: $I_{i} = z_{i} \sum_{j = 1 j \neq i}^{n} w_{ij} z_{j}$

Among them, n is the total number of study areas; z_i and z_j are the normalized observations of the supply levels x_i and x_j of area i and area j, respectively. At a given confidence level, if Ii is significantly greater than 0 and zi is greater than 0, then area i is a high value cluster (HH). If Ii is significantly greater than 0 and zi is less than 0, then area i is a low-valued cluster (LL). If Ii is significantly less than 0 and zi is greater than 0, then area i is an outlier (HL). If Ii is significantly less than 0 and zi is less than 0, then area i is an outlier (LH).

Hot spot analysis can identify spatial clustering of hot and cold spots with statistical significance. Hotspot analysis will look at each feature in the environment of neighboring features. To be a statistically significant hotspot, the feature should have a high value and be surrounded by other features that also have a high value; otherwise, it must be a statistically significant cold. Points, features should have low values and be surrounded by other features that also have low values. The specific calculation formula is: ${Gi}^{*} = \frac{\sum_{j = 1}^{n} w_{ij} x_{j} - \bar{x} \sum_{j = 1}^{n} w_{ij}}{S \sqrt{\frac{n \sum_{j = 1}^{n} w_{ij}^{2} - {(\sum_{j = 1}^{n} w_{ij})}^{2}}{n - 1}}}$ $\bar{x} = \frac{1}{n} \sum_{j = 1}^{n} x_{j}, S = \sqrt{\frac{\sum_{j = 1}^{n} x_{j}^{2}}{n} - (\bar{x})^{2}}$

Among them, x_i is the supply level of area i, w_ij is the spatial weight matrix, and n is the total number of study areas. This method uses the z-score, p-value, and confidence interval (Gi_Bin) to create a new output feature class for each feature in the input feature class. If the feature has a high z-score and a small p-value, it indicates that there is a spatial clustering of hot spots. If the z-score is low and negative and the p-value is small, it means there is a spatial clustering of cold spots. The higher (or lower) the z-score, the greater the degree of clustering. If the z-score is close to zero, it means that there is no obvious spatial clustering.

3.4 Theil index and Gini coefficient

In order to analyze the shortcomings of supply more deeply, considering the decomposability of Theil index and Gini coefficient, this paper chooses these two methods to analyze the regional differences in supply levels.

The Thiel index can decompose the overall difference into intra-group and inter-group differences, and distinguish the contribution of the two differences. When the Theil index is equal to 0, it indicates that the area under investigation has basically reached the state of absolute equalization; the closer the value is to 0, the higher the degree of equalization of resource allocation in the area under investigation, otherwise, the degree of equalization is lower. The specific calculation formula is as follows:

Overall Theil Index: $T = \sum_{i = 1}^{n} X_{i} lg (X_{i} / P_{i})$

Among them, T is the overall Thiel index, X_i is the proportion of the sample county’s supply level value to the total value of the study area; P_i is the proportion of the rural population in each county and the total population in the study area; n is the number of sample counties in Heilongjiang Province.

Theil index decomposition: $T = T_{b} + T_{w}$ $T_{b} = \sum_{j = 1}^{13} X_{j} lg (X_{j} / P_{j})$ $T_{w} = \sum_{j = 1}^{13} X_{j} T_{j}, T_{j} = \sum_{i = 1}^{n} X_{ji} lg (X_{ji} / P_{ji})$

Among them, T_b is the Theil index between 13 cities in Heilongjiang Province; T_w is the Theil index in 13 cities in Heilongjiang Province; X_j is the proportion of the supply level value of the j-th city to the total value of the study area; P_j Is the proportion of the rural population in the j-th prefecture to the total population of the study area; T_j is the Theil index of the j-th prefecture; X_ji is the supply level of the i-th county in the j-th prefecture; The proportion of the total value of the study area; the proportion of the rural population of the i-th county in the j-th city of P_ij to the total population of the j-th study area.

After transforming the overall Theil index equation, the regional difference contribution rate is obtained: $1 = T_{b} / T + T_{w} / T$

By further decomposing Tw / T, we can get the contribution rate of each of the 13 cities to the overall difference.

The Gini coefficient is mainly used to quantitatively measure the average degree of income distribution. It can also decompose the difference in total income between different sub-receivers. The Gini coefficient ranges from 0-1. The 0.4 is usually used as the warning line for the income distribution gap. This article uses the Gini coefficient to analyze the differences in the supply levels of various types of rural basic public services in Heilongjiang Province. The following formulas are commonly used in statistics to study the decomposition and calculation of grouped Gini coefficients: $C_{f} = \sum_{i = 1}^{n} X_{fi} Y_{fi} + 2 \sum_{i = 1}^{n - 1} (1 - V_{fi}) Y_{fi} - 1$

In the formula, C_f is the concentration rate of the supply of basic rural public services of type f. The larger the value, the more uneven the distribution; X_fi is the proportion of the supply of basic public services of type f in the sample counties and districts to the total area of the study area; Yi is the sample The proportion of rural population in counties and districts to the total population in the study area; V_fi is the cumulative proportion from X_f1 to X_fi after ranking by the level of per capita rural basic public service supply, and n is the number of counties in Heilongjiang Province. $G = \sum_{f = 1}^{F} W_{f} C_{f}$

In the formula, G is the Gini coefficient, C_f is the concentration ratio of various types of rural basic public services, W_f is the proportion of various types of rural basic public services in the supply level of rural basic public services, and F is the number of types of rural basic public services.

By calculating and comparing W_fC_f and G, we can determine the contribution trend Q_f of various types of rural basic public services to the Gini coefficient, that is, the degree of the effect of various types of rural basic services on the overall inequality of distribution. It can also be called a certain type of rural basic public services. The percentage of the Gini coefficient that can be explained is calculated as follows: $Q_{f} = W_{f} C_{f} / G$

3.5 Data sources

The sample selected in this article is 82 county-level administrative regions in Heilongjiang Province, including some municipal districts, all county-level cities, counties and autonomous counties. The data comes from the third national agricultural census conducted by Heilongjiang Province in 2017. The standard time of the census is December 31, 2016, and the period data is 2016.

4 Spatial feature and regional differentiation analysis of rural basic public service

4.1 Measurement of the supply level based on TOPSIS model

In order to significantly measure the relative supply level of rural basic public services in counties within Heilongjiang Province, the standard variance level method was used as a reference, and the supply level measurement results in Heilongjiang Province were used as a reference to classify the supply level measurement results. The relative differences in the supply levels of the sample counties are investigated through classification, and the formula is as follows: $D = \frac{{RBPS}_{i} - μ}{σ}$

Among them, RBPS_i is the level of rural basic public service supply level in county i, μ is the average level of rural basic public service supply level in Heilongjiang Province, σ is the standard deviation, and D is the level index. It is divided into 5 units with 0.5 standard deviation as the unit grade. The specific equivalent division is shown in the following Table 2:

Table 2
Classification of supply levels

Criteria for the classification Grade

D≥1 Excellent

0.5≤D<1 Good

–0.5≤D<0.5 Average

–1≤D< -0.5 Poor

D< -1 Bad

Criteria for the classification	Grade
D≥1	Excellent
0.5≤D<1	Good
–0.5≤D<0.5	Average
–1≤D< -0.5	Poor
D< -1	Bad

Combining the entropy method and the calculation principle of TOPSIS operation, using the Heilongjiang Province agricultural census data and the standard level of supply level difference method, the measurement results are summarized as follows. The proportion of 82 counties in Heilongjiang Province among the 5 grades is: excellent grades account for 14.63%, good grades account for 2.44%, average grades account for 47.56%, poor grades account for 28.05%, and bad grades account for 7.32%. After further merging of similar grades, it can be found that the sum of the poor and bad grades is far more than the sum of the excellent and good grades, indicating that the supply gap between regions is very different. Among them, the average supply level of very good counties and districts is 0.3306 and the average supply level of very poor counties and districts is 0.0895, which further proves that the overall supply level polarization characteristics are also obvious.

4.2 Spatial analysis based on data aggregation algorithms

This paper presents a spatial visualization of the basic public service supply level in rural areas of Heilongjiang Province, as shown in Fig. 1. From the perspective of the whole province, the areas with very good supply levels are mainly concentrated in the area around the Ha-Da-Qi urban agglomeration in the southwest and a few areas in the northeast. The regions with poor and very poor supply levels are mainly concentrated in the north and southeast. In terms of cities, Harbin, Qiqihar and Shuangyashan have more counties and districts with good supply levels, and Mudanjiang, Jixi, Hegang, Yichun and Heihe counties have poor levels of supply. There is big gap in the supply levels of different counties and districts within the 13 cities. Harbin, Qiqihar, Shuangyashan, Mudanjiang and Suihua have quite obvious internal polarization characteristics.

Fig. 1

Hierarchical map of rural basic public service supply levels.

The estimated value of the global Moran’s I index calculated is 0.256518. Only less than 1% of the data distribution may be randomly distributed, and the possibility of data aggregation is greater than the probability of random distribution, and it can significantly reject the Assumption. This shows that the spatial distribution of rural basic public service supply levels has a certain agglomeration characteristic, and has a spatial positive correlation pattern. That is, counties with high supply levels tend to be adjacent in space, and counties with low supply water tend to be adjacent in space. This shows that the supply of basic public services in rural areas has a space spillover effect. When the supply level of a county increases, it can positively promote the supply level of surrounding counties.

Anselin Local Moran’s I was used to study the local spatial characteristics. From the analysis results in Fig. 2, we can know that at a significance level of 0.05, there are 7 counties and districts with significant spatial clustering, and 1 county district with outliers. Among them, there are 6 types of high-valued space aggregation (HH) surrounded by high-value. These counties and their surrounding counties have higher levels of rural basic public service supply, which are mainly distributed in the southwest of Heilongjiang Province. The counties, specifically Tailai County, Longjiang County, Gannan County, Yanshou County, Shangzhi City, and Wuchang City, have promoted the development of agriculture and rural areas, and provided solid material conditions for the provision of basic public services in rural areas. There is one type of spatial aggregation (LL) surrounded by low values. The level of rural basic public service supply in Xunke County and surrounding counties is low, and the relatively lagging level of economic development has caused the supply level to remain low. There is one type of anomalous value (LH) surrounded by low values. The rural basic public service supply level in Acheng District is low, while the rural basic public service supply level in surrounding counties is high. This reflects the heterogeneity of the spatial distribution of basic public services in rural areas. From the perspective of equity, the improvement of the future supply level should focus on counties and districts with low spatial aggregation type (LL). In particular, farmers in Acheng District, which is of the type of outliers (LH), is more likely to have a sense of injustice, which should be given high attention and response in the practice of improving the provision of basic public services in rural areas.

Fig. 2

Clustering and outlier distribution of rural basic public services.

In order to further explore the cold and hot spots in the rural basic public service supply level in Heilongjiang Province, the cold and hot spots were analyzed, and the local statistics were classified from high to low into hotspots, sub-hotspots, sub-cold-spots and cold-spots by using the Jenks method. The spatial pattern of cold and hot spots in Heilongjiang’s rural basic public service supply level, as shown in Fig. 3: Overall, there is a marked polarization in the supply level. The proportions of the total were 9.76%, 4.88%, 3.66%, and 2.44%, respectively. The hot spots include 8 counties in Tailai County, Longjiang County, Gannan County, Meris Darhan District, Fangzheng County, Yanshou County, Shangzhi City and Hailin City. Secondary hotspots include Bin County, Shuangcheng District, Acheng District, and Wuchang City. The hotspots and sub-hotspots are mainly concentrated along the Ha-Da-Qi urban agglomeration, with Harbin and Qiqihar being the main counties. Most of these counties are located in the plains. Agriculture and animal husbandry is their leading industry, and it is an important food base in China. The level of agricultural modernization and agricultural industrialization is relatively high, and the characteristic agricultural foundation is good, like Tailai County, Fangzheng County and Wuchang City, etc. The cold spots include 2 counties in Xunke County and Wudalianchi City. The secondary cold spots include 3 counties in Sunwu County, Bei’an City, and Jiayin County. The cold spots and sub-cold spots are mainly concentrated in Heihe City in northern Heilongjiang, of which only Jiayin County is affiliated to Yichun City. These counties are shortcomings in the supply of rural public services in Heilongjiang Province. These areas also need to invest more in the future County of resources.

Fig. 3

Spatial pattern of hot and cold spots in rural basic public service supply levels.

4.3 Analysis of regional differences

Based on the rural basic public service supply level value (RBPS) of the sample counties in Heilongjiang Province, the Theil index was used to further quantify the degree of regional differences. It is shown in Table 3. The overall Thiel index is 0.2270, the thirteen inter-city Thiel index is 0.1014, and the thirteen intra-city Thiel index is 0.1257. The above results indicate that the regional differences in the supply of basic public services in rural Heilongjiang are relatively large. In comparison, intra-regional differences are greater than inter-regional differences, indicating that intra-regional differences are the main influencing factors that constitute regional overall differences, and their contribution to the overall differences. They are 55.35% and 44.65%. However, it should also be noted that intra-regional and inter-regional differences have a greater impact on the overall situation. In the practice of reducing regional differences, no one should be ignored. The 13 intra-regional differences and contribution rates are further decomposed, and the 3 largest cities that contribute the most to the overall difference are Shuangyashan, Mudanjiang, and Harbin. The contribution rates are 25.07%, 12.085%, and 5.37%. The overall difference contribution rate is the smallest in Yichun, with a contribution rate of 0.23%.

Table 3
Theil index and its decomposition for the supply of rural basic public services

Type Theil index Contribution rate

T 0.2270 100.00%

T_b 0.1014 44.65%

T_w 0.1257 55.35%

Harbin 0.0698 5.37%

Qiqihaer 0.0216 1.33%

Jixi 0.0490 0.65%

Hegang 0.1388 2.15%

Shuangyashan 0.6941 25.07%

Daqing 0.0117 0.27%

Yichun 0.0181 0.23%

Jiamusi 0.0524 1.82%

Qitaihe 0.0958 1.25%

Mudanjiang 0.3156 12.08%

Heihe 0.0567 1.37%

Suihua 0.0141 0.78%

Daxing’anling 0.0822 2.98%

Type	Theil index	Contribution rate
T	0.2270	100.00%
T_b	0.1014	44.65%
T_w	0.1257	55.35%
Harbin	0.0698	5.37%
Qiqihaer	0.0216	1.33%
Jixi	0.0490	0.65%
Hegang	0.1388	2.15%
Shuangyashan	0.6941	25.07%
Daqing	0.0117	0.27%
Yichun	0.0181	0.23%
Jiamusi	0.0524	1.82%
Qitaihe	0.0958	1.25%
Mudanjiang	0.3156	12.08%
Heihe	0.0567	1.37%
Suihua	0.0141	0.78%
Daxing’anling	0.0822	2.98%

Based on the supply levels of various types of basic rural public services in the sample counties of Heilongjiang Province, the Gini coefficient method was used to quantify the regional differences in the supply of different types of basic public services in rural areas. According to calculations, the overall Gini coefficient of rural basic public services in Heilongjiang Province is 0.39816, which is close to the standard line of 0.4, and the overall gap is not a large disparity. However, the effects of different types of rural basic public services on the Gini coefficient are quite different. The regional differences in the supply of basic public services in different categories of rural areas are shown in Table 4. The concentration ratios of rural human settlements and transportation and logistics facilities were 0.61086 and 0.54920, respectively, which have far exceeded the disparity standard line 0.4. This shows that the supply of these two types of rural basic public services is quite uneven between regions, and their contribution to the overall Gini coefficient is also ranked first and second respectively, which is the main reason for the difference in overall supply and exacerbates inequality degree. This also verifies the urgency of improving rural human settlements. The concentration rate of farmland water conservancy facilities, basic education in rural areas, healthy rural areas, rural social security and old-age care services are all smaller than the Gini coefficient. Among them, the minimum concentration rate of rural social security and old-age services is only 0.24246. This shows that the supply between regions is relatively balanced, and it also highlights the practical results of the work related to reducing regional supply imbalances over the years. The concentration rate of rural modern energy, drinking water, rural informatization, housing and public cultural and sports services is greater than the Gini coefficient. Although the polarization characteristics are not outstanding, it also exceeds the warning line of 0.4. These should also be important aspects to be taken into account in equalization. In particular, the concentration rate of modern energy in rural areas reached 0.46840, indicating that the gap in supply regions is quite disparate.

Table 4

Decomposition of Gini coefficient for rural basic public services

Tpye	C_f	Q_f
Rural transportation logistics facilities	0.54920	20.71%
Farmland water conservancy infrastructure	0.29627	9.91%
Rural drinking water	0.41654	3.96%
Rural modern energy	0.46840	9.99%
Rural informatization	0.40974	2.11%
Rural basic education	0.23962	6.23%
Healthy country	0.38008	4.81%
Rural social security and pension services	0.24146	12.32%
Rural living environment	0.61086	22.73%
Rural housing security	0.42340	2.58%
Rural public culture and sports	0.42137	4.64%

5 Research conclusions and implications

Based on the sample of 82 counties and districts in Heilongjiang Province and based on the data of the third national agricultural census conducted by Heilongjiang Province in 2017, this article scientifically constructed an evaluation index system for the supply of basic public services in rural areas with county-level administrative districts as the calculation unit. The TOPSIS model, data aggregation algorithm, and Theil index were used to calculate and study the level of rural basic public service supply in the region, analyze the spatial characteristics of supply levels and regional differences, and comprehensively analyze the supply of rural basic public services in Heilongjiang Province. The empirical analysis of this article can be concluded as follows. First, from the perspective of Heilongjiang Province as a whole, the level of supply of rural basic public services is still low, and the polarization of the level of supply is obvious. There are far more counties and districts in poor and bad grades. For counties and districts with excellent and good grades, most counties in the southwest have the highest supply levels, and most counties in the north and southeast have the lowest supply levels. Second, the supply of basic public services in rural areas has produced a spatial spillover effect. The county-level supply levels have agglomeration characteristics in spatial distribution, with significant spatial differences. High-value spatial clustering occurs in counties with higher economic levels and better agricultural foundations. It is mainly distributed in some counties and districts of Harbin and Qiqihar. The cold spots are mainly concentrated in the districts of Heihe. Third, from the perspective of different cities, the regional differences in the level of basic public service provision in the rural areas of Heilongjiang Province are more due to intra-regional differences. Further analysis shows that Shuangyashan, Mudanjiang, and Harbin contribute the most to regional differences. Fourth, in terms of different types, the overall gap in rural basic public services in Heilongjiang Province is quite different, but the regional differences in rural human settlements and transportation and logistics facilities are very large, which is a weak link in the supply of basic public services in rural areas.

The research results show that at this stage, the supply of basic public services in rural Heilongjiang Province still faces many challenges. Therefore, governments at all levels should correctly understand the distribution characteristics of supply levels, fully understand the actual conditions of counties and districts, rationally allocate supply resources in a planned way, and strive to achieve equalization of basic public services in urban and rural areas.

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Spatial feature analysis of rural basic public service supply based on TOPSIS model and Data aggregation algorithm

Abstract

Keywords

1 Introduction

2 Related work

3 Evaluation system and research method

3.1 Construction of indicator system

3.3 Data aggregation algorithm and exploratory spatial data analysis

3.4 Theil index and Gini coefficient

3.5 Data sources

4 Spatial feature and regional differentiation analysis of rural basic public service

4.1 Measurement of the supply level based on TOPSIS model

Table 2 Classification of supply levels Criteria for the classification Grade D≥1 Excellent 0.5≤D<1 Good –0.5≤D<0.5 Average –1≤D< -0.5 Poor D< -1 Bad

References

Table 2
Classification of supply levels

Criteria for the classification Grade

D≥1 Excellent

0.5≤D<1 Good

–0.5≤D<0.5 Average

–1≤D< -0.5 Poor

D< -1 Bad