[Table 3]

2.6 Spatial autocorrelation analysis

Spatial autocorrelation was conducted to explore the spatial associations between UI and EHI in China. Global bivariate Moran’s I was adopted to investigate spatial correlations of EHI and UI across the entire study areas, while bivariate local indicators of spatial association (LISA) mainly focused on evaluating the local spatial correlations within different spatial units, such as cities in this study (Cui, 2019). Moreover, the statistical significance of bivariate Moran’s I was assessed by permutation tests, and 999 permutations were used in this study. The significance value for spatial correlation between EHI and UI was set at <0.05 for the obtained pseudo value.
The generated clustering graph could be divided into four agglomeration types, namely H-H (High-High), L-L (Low-Low), H-L (High-Low) and L-H (Low-High). H-H clustering indicates high EHI values surrounded by high UI values; H-L clustering indicates high EHI values surrounded by low UI values; L-H clustering indicates low EHI values surrounded by high UI values; and L-L clustering indicates low EHI values surrounded by low UI values. The spatial autocorrelation between EHI and UI was analyzed with the help of GeoDa 1.20 in this paper. The formulas for calculating Moran’s I are shown below.
\(I_{\text{eu}}=\ \frac{n\sum_{i}^{n}{\sum_{j\neq i}^{n}{W_{\text{ij}}x_{i}^{e}x_{j}^{u}}}}{(n-1)\sum_{i}^{n}{\sum_{j\neq i}^{n}W_{\text{ij}}}}\)(10)
\({I^{\prime}}_{\text{eu}}=\ \ x^{e}\sum_{j=1}^{n}{W_{\text{ij}}x_{\text{ij}}^{u}}\)(11)
where Ieu and I’eu are the global and local bivariate Moran’s I for EHI and UI, respectively.n denotes the total number of spatial units.Wij is an N-by-N spatial weight matrix for measuring spatial correlation between the ith andjth spatial unit, which is generated based on queen contiguity weight with a first order of neighbor in a 3 × 3 matrix. xie andxju denote the standardized value of EHI and UI for the ith andjth spatial units, respectively, which are calculated by Eq. (1).

2.7 Statistical analysis

Partial least squares structural equation modeling (PLS-SEM) combines principal component analysis and multiple regression. It has the advantages of small sample size, prediction of key target structures, and construction of complex structural models, which is widely used in the study of multi-factor causal relationships (Heir, 2019). In this paper, PLS-SEM was utilized to evaluate the essential factors affecting UI and EHI distributions and changes. To explore the correlation among these variables in PLS-SEM preliminarily, the correlation analysis was used with the help of the ”corr” package of R software. EHI, UI, social factors, economic factors, climate, and topography were used as latent variables to construct the PLS-SEM collectively. Then, we established the indicator loading for latent variables, and the hypothesized relationships between exogenous variables (social factors, economic factors, climate, and topography) and endogenous variables (EHI and UI) were calculated as path coefficients. Moreover, bootstrapping analysis in the PLS-SEM setting can be used to test the stability of the estimated model parameters. Each variable was log-transformed to reduce the difference by an order of magnitude.
The measurement model is a prerequisite for SEM, which relates measurement items to their respective latent variables (Munim, 2020). The indicator loadings were recommended above 0.708, which indicated that the construct explained more than 50% of the indicator variance, providing acceptable item reliability (Hair, 2019). Furthermore, we used the average variance extracted (AVE) for all items on each construct to evaluate the convergent validity of each construct measure. An acceptable AVE of 0.50 or higher indicated that the construct explains at least 50% of the variance of its items (Hair, 2019). The construction and estimation of PLS-SEM model were processed using the ”plspm” package of R software (version: 3.6.3).