*2.4. Entropy Method*

Too many variables will likely lead to multicollinearity problems, and in this study, we will develop a multidimensional, innovation agglomeration-based indicator system that can facilitate land use transition. The entropy method is an effective method for evaluating comprehensive indicators. It can effectively reduce the dimensionality of indicators and give higher weights to secondary indicators with greater entropy (degree of variation), thus obtaining an efficient composite indicator. A brief calculation of the entropy method is as follows:

Step 1. A standardised matrix of indicator evaluation systems (c ab,t) is created. where a is the cross-sectional individual a (1 ≤ a ≤ n); b is the indicator b (1 ≤ b ≤ k), and t is the period t.

$$\mathbf{c}'\_{\mathbf{a}\mathbf{b},\mathbf{t}} = \mathbf{c}\_{\mathbf{a}\mathbf{b},\mathbf{t}} - \min\_{\mathbf{k}} |\mathbf{c}\_{\mathbf{a}\mathbf{b},\mathbf{t}}| \left/ \max\_{\mathbf{k}} |\mathbf{c}\_{\mathbf{a}\mathbf{b},\mathbf{t}}| - \min\_{\mathbf{k}} |\mathbf{c}\_{\mathbf{a}\mathbf{b},\mathbf{t}}| \right. \tag{8}$$

Step 2. Formula (9) is the calculation of the information entropy (Eb,t) for the indicator b in period t, and Formula (10) is the calculation of the weight for the indicator b in period t (weightb,t).

$$\begin{array}{l} \text{E}\_{\text{b},\text{t}} = -\ln(\text{n})^{-1} \sum\_{\text{t}=1}^{\text{n}} \left( \text{P}\_{\text{ab},\text{t}}' \right) \ln \left( \text{P}\_{\text{ab},\text{t}}' \right) \\ \text{s.t.} \; \text{P}\_{\text{ab},\text{t}}' = \text{c}\_{\text{ab},\text{t}}' / \sum\_{\text{a}=1}^{\text{n}} \text{c}\_{\text{ab},\text{t}}' \end{array} \tag{9}$$

$$\text{weight}\_{\text{b,t}} = 1 - \text{E}\_{\text{b,t}} \Big/ \mathbf{b} - \sum \text{E}\_{\text{b,t}} \tag{10}$$

#### **3. Design of Variables and Models**
