List

Entropy Method

Entropy Method is a commonly used multi-index evaluation method that determines indicator weights by calculating the information entropy of each index. It is located in SPSSAU -> Comprehensive Evaluation -> Entropy Method.

SPSSAU Operations

To begin, drag the analysis items to the right-side box and click 'Start'. SPSSAU provides two parameters: Composite Score and Non-negative Shift.

Composite Score: When selected, SPSSAU saves the composite score as a new title, named similarly to "CompScore_****".

Non-negative Shift: When selected, if any column contains values ≤ 0, a shift of the absolute value of the minimum plus 0.01 is applied. This ensures all data remain positive for proper calculations.

SPSSAU Data Format

Entropy Method determines the weight distribution of indicators. Each indicator occupies one column of data. The sample ID in the figure is for identification purposes only and is not required for analysis.

Algorithm

1.Data Standardization

Original data must often be standardized to eliminate dimensional effects. Common methods include Range Normalization and Z-score (S).

Note:

SPSSAU does not provide built-in standardization for the entropy method. Researchers can use SPSSAU -> Data Processing -> Generate Variables to apply these methods.

Range Normalization ${x_{i j}}^{'} = \frac{x_{i j} - min (x_{j})}{max (x_{j}) - min (x_{j})}$
Z-score (S) ${x_{i j}}^{'} = \frac{x_{i j} - {\bar{x}}_{j}}{s_{j}}$
${\bar{x}}_{j}$ is the mean and s_j is the standard deviation of indicator j.

2.Non-negative Shift

$x_{i j} = | min (x_{* j}) | + 0.01$

If selected and required, the system applies the above shift.

3.Calculate Proportions

$p_{i j} = \frac{{x_{i j}}^{'}}{\sum_{i = 1}^{m} {x_{i j}}^{'}}$

m is the number of samples and p_ij represents the proportion of sample i in indicator j.

4.Calculate Entropy

$E_{j} = - k \sum_{i = 1}^{m} p_{i j} \ln (p_{i j})$ $k = \frac{1}{\ln (m)}, E_{j}$ is the entropy for indicator j.

5.Calculate Redundancy

$d_{j} = 1 - E_{j}$

6.Calculate Weights

$w_{j} = \frac{d_{j}}{\sum_{j = 1}^{n} d_{j}}$ w_j represents the weight of indicator j, and n is the number of indicators.

7.Composite Score

$S_{i} = \sum_{j = 1}^{n} w_{j} {x_{i j}}^{'}$ S_i is the composite score of sample i.

Note:

If Non-negative Shift is applied, SPSSAU calculates the composite score based on the adjusted data. The comprehensive score is saved as a new title similar to "CompScore_****".

References

【1】The SPSSAU project (2024). SPSSAU. (Version 24.0) [Online Application Software]. Retrieved from https://www.spssau.com.

【2】周俊,马世澎. SPSSAU科研数据分析方法与应用.第1版[M]. 电子工业出版社,2024.

【3】陈伟, 夏建华. 综合主、客观权重信息的最优组合赋权方法[J]. 数学的实践与认识, 2007, 37(001):17-22.