Evaluation - rank sum ratio comprehensive evaluation

1、 effect

rsr （RSR） It refers to ranking benefit indicators from small to large 、 Cost indicators are ranked from large to small , Then calculate the rank sum ratio , Finally, statistical regression 、 Grading sort . By rank transformation , Get dimensionless Statistics RSR, With RSR Value is used to sort the evaluation objects directly or by grades , So as to make a comprehensive evaluation of the evaluation object .

2、 Input / output description

Input : At least two or more quantitative variables .
Output : Reflect the comprehensive scores and grades of the assessment indicators in the quantitative evaluation
 

3、 Case example

Based on a province 6 The scientific and technological input of prefecture level cities , Scientific and technological output , The overall scientific and technological progress shall be comprehensively evaluated by three indicators .

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4、 Modeling steps

1. Construct matrix ： Suppose the evaluation object is n individual , The evaluation index is m individual , Build data matrix (n ×m）.

2. Rank matrix ：
（1） Whole rank sum ratio method ： take n Of two evaluation objects m The evaluation indexes are arranged into n That's ok m Original data table for Columns . Compile the rank of each index and each evaluation object ( order ), Among them, the benefit type indicators are ranked from small to large , Cost indicators are ranked from large to small , Average rank of the same index data . Get the rank matrix , remember  

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（2） Non integral rank sum ratio method ： To improve RSR The deficiency of rank method , There is a quantitative linear correspondence between the compiled rank and the original index value , To overcome RSR It is easy to lose the quantitative information of the original index value when ranking the method .
For benefit indicators ：

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For cost indicators ：

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3. Calculate the RSR ： 

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It's No i The... Of the first object j Rank of indicators , It means the first one j The weight of each indicator , The weight sum is 1. The greater the value of , It indicates that the better the evaluation object is .

4. Calculate the unit of probability

● take WRSR Values are arranged in descending order ;
● List the frequency of each group ;
● Calculate the cumulative frequency of each group ;
● Identify groups WRSR Rank of R And average rank R-;
● Calculate the downward cumulative frequency R- / n × 100 %, The last item is ( 1 − 1 / 4 n ) × 100 % correct ;
● According to the cumulative frequency , Inquire about “ Comparison table of percentage and probability unit ”, Find the corresponding probability unit Probit value ;
PS： Detailed comparison table of percentage and probability unit ：https://s0.spsspro.com/resources/images/ Comparison table of percentage and probability unit .png

5. Calculate the linear regression equation  

Use... In the table WRSR The distribution value is used as the dependent variable ,Probit Value as argument , Do a linear regression , And carry out regression analysis .

6. Grading sort

Calculated according to the regression equation WRSR The evaluation objects are sorted according to the estimated value .