This article will explain some common issues in weight calculation:How to calculate the comprehensive weight value of the combined weighting method? How to calculate multi-level weights? How can the weights calculated by multiple methods be combined into comprehensive weights for subsequent analysis? Common combinations of different weight calculation methods?
1. Review of nine weight calculation methods
The choice of weight calculation method is a top priority in the construction of the rating index system, and different methods have different calculation principles. In the actual analysis process, appropriate weight calculation should be selected based on data characteristics and professional knowledge.
Nine commonly used weight calculation methodsThe characteristics are as follows:
For detailed instructions on the weight calculation method, please refer to previous issues:
Collection of useful information→Nine weight calculation methods
Graduation thesis | Summary of 13 weight calculation related methods
2. Combination empowerment method
Each weight calculation method has its scope of application.Sometimes it is necessary to use multiple methods to measure the weight of the same data. This is called the combined weighting method, so that the comprehensive weight performance is higher and can better reflect the real characteristics of the data.
Example: Use the entropy method and the AHP method at the same time. The AHP method can reflect the experience of experts on different indicators, and the entropy method can reflect the information characteristics provided by the data itself. , the combined use of the two can not only reduce the subjectivity of AHP method weighting, but also reduce the fluctuation of weights caused by data changes.
With so many weight calculation methods used in combination, how to get the weight value (comprehensive weight) of the combined weighting method? Usually according to different weight combination methods, the discussion can be divided into the following two situations:
1. The two weight calculation methods have the same principle.
Case 1:The two weight calculation methods have the same principle and belong to the same type of method. Then the average value can be calculated at this time, and the result is the weight value of the combined weighting method.
Example: AHP analytic hierarchy process and order chart method, are both subjective assignment methods. They use the size of numbers to calculate the weight. At this time, the average of the two can be calculated as the comprehensive weight.
For example, if you use the AHP analytic hierarchy process to get the weight value of indicator A1 to be 0.1, and use the ranking diagram method to get the weight value of indicator A1 to be 0.2, then the combined weighting method of the two to get the comprehensive weight of indicator A1 is: WA1 = (0.1+ 0.2)/2=0.15. The weight values of other indicators can be calculated in the same way.
2. The calculation principles used by the two weights are different.
Case 2:The calculation principles used by the two weights are different, and the data characteristics used are also inconsistent. At this time, there is more than one way to calculate the comprehensive weight. It is recommended to use References shall prevail.
- Example 1: Calculate weight by entropy method and AHP method
One is the subjective assignment weight, and the other is the objective assignment weight. Combining the two methods makes the data obtained more reflective of the actual situation. Commonly used formula: W=A*B/ (∑A*B). A and B are the weights obtained by two methods. The calculation process is as follows:
In addition, there are other calculation formulas, such as W=(A+B)/∑(A+B) , please refer to relevant references for details.
- Example 2: Principal components and AHP analytic hierarchy process
Commonly used formula: W=tA+(1-t)B. A and B are the weights obtained by the two methods, and t is the weight coefficient. The value of t is between 0 and 1, which depends on the degree of difference in the weight of each indicator in the AHP method (or refer to relevant literature).
- If the weight difference between the indicators in the AHP method is not large, t should be smaller.
- If the weight difference between the indicators in the AHP method is large, t should be larger.
- If the calculation results of the two methods are not significantly different, the t value defaults to 0.5.
For example, when the t value is 0.3, the comprehensive weight of the A1 indicator is: WA1=0.3*0.1+(1-0.3)*0.2=0.17. The calculation process of other indicators can be deduced in the same way.
Supplement: Determination of weight coefficient
The determination of the weight coefficient is not limited to one method. For details, please refer to relevant references. For example, in Li Liangchen's "Research on the Evaluation of PPP Operation Capabilities of State-owned Construction Enterprises Based on Combination Empowerment", the weight coefficient determination method is as follows:
Li Liangchen. Research on PPP operation capability evaluation of state-owned construction enterprises based on portfolio empowerment[D]. Zhengzhou University, 2022.
Another example is the distance function method used in "Risk Assessment of Debris Flows in the Jinsha River Basin by Combination Weighting Method" by Zhang Chen et al. The process of determining the weight coefficient is as follows:
Zhang Chen, Wang Qing, Chen Jianping, Gu Fuguang, Zhang Wen. Risk assessment of debris flow in Jinsha River basin using combined weighting method [J]. Geotechnical Mechanics, 2011, 32(03): 831-836.
To sum up, when using the combined weighting method to calculate the comprehensive weight, the above only provides some common and relatively simple calculation methods. The specific comprehensive weight calculation should be References shall prevail.
3. Multi-level weight calculation
In multi-level comprehensive evaluation research, it is not only necessary to calculate the weight of first-level indicators, but also the weight of second-level indicators, and even the weight of third-level indicators. So how should it be calculated?
1. Give examples
Take the full text using the AHP analytic hierarchy process to calculate weights as an example: There is such a research that needs to build an employee performance evaluation system. The evaluation index system as shown below is designed and scored by experts. Data collection. The AHP method is now used to calculate the weights of each level, and the evaluation system is used to calculate the comprehensive score of each employee.
step1: Calculate the weight of the first-level indicator (or calculate the weight of the second-level indicator first)
During analysis, the weight of each layer needs to be calculated separately. First use SPSSAU [Comprehensive Evaluation]--[AHP Hierarchical Analysis] to calculate the weight of the first-level indicators "Work Attitude", "Learning Ability", "Work Ability" and "Team Collaboration". Fill in the table with expert scoring results:
SPSSAU outputs the AHP analytic hierarchy process results as follows:
step2: Calculate the weight of secondary indicators
The same method is used to calculate the secondary indicator weight. For example, calculate the weight of each indicator (A1, A2, A3) under "Work Attitude":
By analogy, the weights of the second-level indicators subordinate to the first-level indicators are calculated. Finally, manually multiply the weights of the plan layer and the criterion layer to obtain the final weight value of each plan layer. This weight represents the "normalized weight" (That is, the weight when the sum of the weights of the minimum indicator layer is 1, which represents the weight when compared from the perspective of the factor layer).
For example, the calculated first-level indicator weights are 0.30, 0.15, 0.30, and 0.25 respectively. The weight of the secondary indicator A1 is 0.23, so the final weight value of A1 is 0.30*0.23=0.069. Then useweight*score to get the employee's comprehensive score.
2. Weight combination method
There are some combinations of commonly used weight calculation methods, such as AHP and entropy method, principal component and entropy method, etc. AHP or principal component method may be used as a first-level indicator weight method. The entropy method is used as a method for weighting secondary indicators.
Such a combination weight is still used during analysis to obtain the first-level weight and the second-level weight respectively, and then multiply the first-level weight and the second-level weight to obtain a value that can be used for analysis and calculation The weight of each indicator. If third-level indicators are involved, the calculation process is similar.