Critic Weight

Criteria Importance Through Intercriteria Correlation (CRITIC) weight algorithm is a method used for multi-indicator decision analysis. It calculates weights by considering both the correlation between indicators and their standard deviations. It is located in SPSSAU -> Comprehensive Evaluation -> Critic Weight.

SPSSAU Operations

Drag the analysis items to the right box and click 'Start'. SPSSAU includes one parameter: Composite Score.

Composite Score: When selected, SPSSAU will save the comprehensive score under a new title, named similarly to "CompScore_****".

SPSSAU Data Format

CRITIC weights are used to calculate indicator weights. Each indicator occupies one column. The sample number in the diagram is only for reference and does not affect the analysis.

Algorithm

1.Data Preparation

Collect and organize the indicator data for analysis, constructing a data matrix X where each row represents a research object and each column represents an indicator.

2.Standardization of Data Matrix

To eliminate the impact of units, the data matrix is standardized using the following method:

$$x_{ij}^{\prime }=\frac{x_{ij}-min(x_j)}{max(x_j)-min(x_j)}$$

x_ij is the original data, and x_{ij}^{\prime } is the standardized data.

3.Calculate Variability Indicators

The standard deviation of each indicator is calculated as:

$${\sigma }_j=\sqrt{\frac{1}{m-1}\sum _{i=1}^m({x_{ij}}^{\prime }-\overline{x_{j^{\prime }}}{)}^2}$$

m is the number of research objects, and \overline{x_{j^{\prime }}} is the mean of indicator j. The larger this value, the greater the weight.

4.Calculate Conflict Indicators

The correlation matrix between indicators (R) is calculated using Pearson Correlation Coefficient:

$$r_j=\frac{\sum _{i=1}^m({x_{ij}}^{\prime }-\overline{x_{j^{\prime }}})({x_{ik}}^{\prime }-\overline{x_{k^{\prime }}})}{\sqrt{\sum _{i=1}^m({x_{ij}}^{\prime }-\overline{x_{j^{\prime }}}{)}^2\sum _{i=1}^m({x_{ik}}^{\prime }-\overline{x_{k^{\prime }}}{)}^2}}$$

Then, the conflict indicator is calculated as:

$$\sum _{k=1}^m(1-r_{kj})$$

A higher correlation reduces the conflict indicator and subsequently lowers the final weight.

5.Calculate Information Amount

Weights are calculated using:

$$w_j={\sigma }_j\times \sum _{k=1}^m(1-r_{kj})$$

w_j represent the weight of indicator j.

6.Calculate Weights

The weights are normalized so that their sum equals 1:

$${w_j}^{\prime }=\frac{w_j}{\sum _{j=1}^n{w}_j}$$

7.Calculate Composite Score

The composite score is calculated as:

$$CompScor{e}_i=\sum _{j=1}^n{w}_j\times x_{ij}$$

• Explanation:
• CompScore_i represents the composite score of item.
• w_j represents the weight of indicator j.
• x_ij represents the score of item on indicator j.
• n represents the number of evaluation indicators.