2.2.1. Entropy Method

The entropy method is one of the common composite indicator measures. The entropy method assigns weights based on the degree of variation between variables, and the greater the variation, the greater the weight. The entropy method has the feature of reducing the dimensionality of variables and mitigating the presence of multicollinearity between variables [45]. The entropy method is calculated as follows:

Step 1. Obtain a standardized matrix of indicators (*Eit*,*<sup>k</sup>*) where *eit*,*<sup>k</sup>* is the matrix of unprocessed indicators, *i* indicates the region *i*, *t* indicates the year *t, k* indicates the *k*th indicator, with a total of *K* indicators.

$$E\_{it,k} = \frac{|\varepsilon\_{it,k} - \min\_{\mathcal{K}}|\varepsilon\_{it,k}|}{\max\_{\mathcal{K}}|\varepsilon\_{it,k}| - \min\_{\mathcal{K}}|\varepsilon\_{it,k}|} \tag{1}$$

Step 2. Calculate the information entropy (*It*,*<sup>k</sup>*). Calculate *<sup>E</sup> it*,*<sup>k</sup>* by Equation (2), where *n* is the total number of regions. Additionally, calculate *It*,*<sup>k</sup>* by Equation (3).

$$E\_{\text{it},k} = \frac{E\_{\text{it},k}}{\sum\_{i=1}^{n} E\_{\text{it},k}} \tag{2}$$

$$I\_{t,k} = -\ln(n)^{-1} \sum\_{i=1}^{n} E\iota\_{it,k} \* \ln(E\iota\_{it,k}) \tag{3}$$

Step 3. Calculate the weight matrix (*Wt*,*<sup>k</sup>*) by Equation (4).

$$\mathcal{W}\_{t,k} = \frac{1 - I\_{t,k}}{K - \sum I\_{t,k}} \tag{4}$$

#### 2.2.2. Map Visualization of Data

Map visualization of data is a type of exploratory spatial data analysis (ESDA), whose main purpose is to present spatial geographic attributes and data information more clearly to the reader, usually through software such as ArcGIS [46], where spatial data are embedded in a geographic map. However, traditional studies of regional economics, geography economics, etc. usually analyze data through such visualization methods, which are qualitative in nature and have a certain non-objectivity. Moreover, this method cannot verify the causal relationship between the dependent and independent variables. For example, in this study, we are only able to theorize that there is a causal relationship between economic efficiency of land and environmental pollution improvement, and we are unable to obtain quantitative support.
