In 2014, more than 800,000 poor people were registered in Linyi, Shandong, with the poverty incidence in each township ranging from 0·001 to 0.711. Spearman's correlation coefficient was performed to quantify the magnitude of variables and poverty incidence. A strongest positive correlation was observed between poverty incidence and per capita cultivated area (r = 0.661, p < 0·0001; table 1).
Table.3 Spearman's correlation coefficient
Var | Cor | p |
ME | 0.341 | < 0.0001 |
MS | 0.46 | < 0.0001 |
PCA | 0.661 | < 0.0001 |
PGA | 0.322 | < 0.0001 |
RND | -0.493 | < 0.0001 |
MTG | 0.455 | < 0.0001 |
RD | -0.383 | < 0.0001 |
Since spatial poverty is structured by geography and economy, we also sought to explore the variables that might be associated with the characteristic of spatial poverty over space. Results from the global model (Table.3) are first summarized to provide context for the GWR results. We applied the ordinary least square (OLS) to identify the global correlation. As shown in Table.3, per capita cultivated land had a significant positive correlation in all main effects (0.661, p < 0.01). Only two interacting variables suggested a significant effect (PCA*RD, 0.215, p < 0.05; PCA*RND, -0.504, p < 0.01). Based on a standard t-value threshold of 1.96 for a 95% confidence level, only three variables were statistically non-zero. The most influential variable is the per capita cultivated land area, which has a relatively strong globally positive relationship with poverty incidence, followed by per capita grassland area. In contrast, the most influential negative association is with road network density, followed by the mean elevation, river density, and mean time cost to local government.
Table.4 Result of OLS
Var | Estimate | SE | t.value | p-value |
lnME | 0.1171 | 0.1811 | 0.6467 | 0.5188 |
lnMTG | 0.0612 | 0.2751 | 0.2224 | 0.8243 |
lnRD | -0.0750 | 0.0686 | -1.0932 | 0.2761 |
lnPCA | 1.0969 | 0.2075 | 5.2859 | 0.0000 |
lnRND | -0.1955 | 0.1644 | -1.1892 | 0.2363 |
lnPGA | 0.0010 | 0.0463 | 0.0215 | 0.9829 |
lnME:lnPCA | -0.2395 | 0.2699 | -0.8873 | 0.3764 |
lnMTG:lnPCA | 0.1039 | 0.1365 | 0.7607 | 0.4481 |
lnRD:lnPCA | 0.2706 | 0.1194 | 2.2671 | 0.0249 |
lnPCA:lnRND | -0.4758 | 0.1691 | -2.8137 | 0.0056 |
The result of OLS has the limitation of providing local statistics for spatial data. We entered all variables into the GWR model simultaneously to explore the relationship between them and the dependent variable, poverty incidence. Adaptive bandwidth was applied in this research due to vulnerability to extreme coefficients(Cho et al. 2009). Table.5, Table.6, and Fig. 4 present the local statistic result. In concordance with the global model results, four variables had a positive association (ME, PCA, MTG*PCA, RD*PCA) with poverty incidence across the study area, while three variables had a negative association with poverty incidence across the study area (RD, RND, RND *PCA). The value of PGA both presents a low effect in the global model (0.0003, p > 0.1) and local model (-0.004-0.047). The PGA coefficient's negative value appears in the study area's southern boundary area, which may be the result of the extreme coefficient in geographical weighted regression(Cho et al. 2009). The two variables in global regression suggested a non-significant correlation, but the direction and magnitude of coefficients vary significantly in the study area (MTG, -0.330-0.475; ME*PCA, -0.608-0.178).
The first category (Fig. 4) consists of those surfaces that are the main effect (ME, MTG, RD, PCA, RND, PGA). The coefficient of ME (global model, 0.1171, p = 0.5188; local model, 0.050–0.190), RD (global model, -0.0750, p = 0.2761; local model, -0.152–0.035), PCA (global model, 1.0969, p < 0.01; local model, 0.961–1.348) and RND (global model, -0.1955, p = 0.2363; local model, -0.312–0.151) had consistent direction from global model and local model which do not display significant spatial variation. MTG has a statistically non-significance of parameter estimates (0.0612, p = 0.8243) because of spatial variation of parameter estimates on account of spatial non-stationarity (-0.330-0.475).
The second category (Fig. 4) consists of those interacting effect surfaces (PCA*ME, PCA*MTG, PCA*RD, PCA*RND). PCA*ME is not a significant variable in the global model (0.0612, p = 0.8243) due to spatial non-stationarity (-0.608-0.178). The result of RD*PCA (global model, 0.2706, p = 0.0249; local model, 0.237–0.338) and RND*PCA (global model, -0.4758, p = 0.0056; local model, -0.697–0.404) observed that they have a significant global effect because of the same direction of a parameter in the local model. The coefficients of MTG*PCA do not change much, and the value remains low (global model, 0.1039, p = 0.4481; local model, 0.046–0.137).
Table.5 result of geographically weighted regression
Var | Mean | Sd | Median | Min | Max | Range |
lnME | 0.105 | 0.034 | 0.099 | 0.050 | 0.190 | 0.140 |
lnMTG | 0.101 | 0.268 | 0.150 | -0.330 | 0.475 | 0.806 |
lnRD | -0.100 | 0.036 | -0.108 | -0.152 | -0.035 | 0.117 |
lnPCA | 1.156 | 0.115 | 1.164 | 0.961 | 1.348 | 0.387 |
lnRND | -0.228 | 0.039 | -0.215 | -0.312 | -0.151 | 0.161 |
lnPGA | 0.022 | 0.014 | 0.024 | -0.004 | 0.047 | 0.050 |
lnME:lnPCA | -0.226 | 0.243 | -0.246 | -0.608 | 0.178 | 0.786 |
lnMTG:lnPCA | 0.092 | 0.026 | 0.089 | 0.046 | 0.137 | 0.091 |
lnRD:lnPCA | 0.298 | 0.028 | 0.306 | 0.237 | 0.338 | 0.101 |
lnPCA:lnRND | -0.560 | 0.082 | -0.577 | -0.697 | -0.404 | 0.293 |
During the study, it is found that the distribution of elevation has a strong correlation with the distribution of coefficients. We applied the hierarchical geographically weighted regression out of consideration of the hierarchical effect of elevation. Table.6 shows the results from the global model and hierarchical geographically weighted regression group by the median of ME. The coefficients of the four variables keep the same direction, including RD (global, -0.152–0.035; low elevation, -0.112–0.065; high elevation, -0.111–0.081), PCA (global, 0.961–1.348; low elevation, 2.344–2.517; high elevation, 1.526–1.646), RD*PCA (global, 0.237–0.338; low elevation, 0.481–0.516; high elevation, 0.200-0.238), PGA (global, -0.004-0.047; low elevation, 0.005–0.017; high elevation, 0.016–0.036). The parameter estimation of MTG (global, -0.330-0.475; low elevation, 0.348–0.509; high elevation, -0.85–0.76) and ME*PCA (global, -0.608-0.178; low elevation, 1.926–2.098; high elevation, -0.75–0.57) present spatial heterogeneity in global model and different direction in hierarchical geographically weighted regression. The coefficients of RND (global, -0.312–0.151; low elevation, -0.146-0.044; high elevation, -0.543–0.487) present different variations in the model of low elevation but just no significant spatial heterogeneity. The results of MTG*PCA (global, 0.046–0.137; low elevation, -0.054–0.004; high elevation, 0.822–0.959) and RND*PCA (global, -0.697–0.404; low elevation, -1.043–0.965; high elevation, 0.46–0.536) present consistent direction in the global model but different directions appear in the results of the hierarchical model, which indicate that the effect of PCA on PI is greater for the low value of RND or MTG in low elevation and greater for the high value of RND or MTG in high elevation.
Table.6 the min and max value of coefficient from three model
Var | global | low elevation | high elevation |
min | max | min | max | min | max |
lnMTG | -0.330 | 0.475 | 0.348 | 0.509 | -0.85 | -0.76 |
lnRD | -0.152 | -0.035 | -0.112 | -0.065 | -0.111 | -0.081 |
lnPCA | 0.961 | 1.348 | 2.344 | 2.517 | 1.526 | 1.646 |
lnRND | -0.312 | -0.151 | -0.146 | 0.044 | -0.543 | -0.487 |
lnPGA | -0.004 | 0.047 | 0.005 | 0.017 | 0.016 | 0.036 |
lnME:lnPCA | -0.608 | 0.178 | 1.926 | 2.098 | -0.75 | -0.57 |
lnMTG:lnPCA | 0.046 | 0.137 | -0.054 | -0.004 | 0.822 | 0.959 |
lnRD:lnPCA | 0.237 | 0.338 | 0.481 | 0.516 | 0.200 | 0.238 |
lnPCA:lnRND | -0.697 | -0.404 | -1.043 | -0.965 | 0.46 | 0.536 |