Rank sum ratio comprehensive evaluation method for common models in mathematical modeling

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

Case study ： To a province 10 A comprehensive evaluation of the three indicators of maternal health care in four regions

4、 Case data

Rank sum ratio comprehensive evaluation method (RSR) Case data

5、 Case operation

Step1： New analysis ;
Step2： Upload data ;
Step3： Select the corresponding data to open and preview , Click start analysis after confirmation ;

step4： choice 【 Rank sum ratio comprehensive evaluation method 】;
step5： View the corresponding data format ,【 Rank sum ratio comprehensive evaluation method 】 The characteristic sequence is required to be a quantitative variable , It is divided into positive indicator variables and negative indicator variables , And the sum of the number of positive indicator variables and negative indicator variables is greater than or equal to two items .
step6： Set the rank editing method （ Non integral rank method （ Recommended ）、 Whole rank method 、 No treatment ）、 Number of grades （3 files 、4 files 、5 files ）、 Variable weight （ Entropy weight method 、 Do not set the weight 、 Custom weights ）.
step7： Click on 【 To analyze 】, Complete the operation .

6、 Output result analysis

Output results 1： Index weight calculation

Chart description ： The weight calculation results of entropy weight method show that , The weight of antenatal examination rate is 29.447%、 The weight of maternal mortality is 36.344%、 The weight of perinatal mortality is 34.209%, The maximum weight of the index is the maternal mortality （36.344%）, The minimum value is the antenatal examination rate （29.447%）.

Output results 2： Rank value calculation

analysis ：X1、X2、X3 It is the result of normalizing the original data in the same direction ,R1、R2、R3 The result of non integral rank coding on the original data .

Output results 3：RSR Distribution table

Chart description ： The purpose of the above table is to calculate Probit value ,Probit The value is based on the percentage （ Evaluation rank number /n*100%） stay “ Comparison table of percentage and probability unit ” Got .
● take RSR Values are arranged in descending order ;
● List the frequency of each group ;
● Calculate the cumulative frequency of each group ;
● Identify groups RSR 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 ;
● Use... In the table RSR Distribution values as independent variables ,Probit Value as dependent variable , Do a linear regression , The results are shown in the table below .
PS： Detailed comparison table of percentage and probability unit ：https://s0.spsspro.com/resources/images/ Comparison table of percentage and probability unit .png

Output results 4： Linear regression

*p<0.05,**p<0.01,***p<0.001
analysis ： The probability unit value corresponding to the cumulative frequency Probit Independent variable , With RSR The value is the dependent variable , Calculate the regression equation .
from F The analysis of the test results can lead to , Significance P The value is 0.001**, The level is significant , The regression coefficient is rejected 0 The original hypothesis of , At the same time, the goodness of fit of the model R² by 0.763, The model performs well , Therefore, the model basically meets the requirements . For the collinearity of variables ,VIF All less than 10, So the model has no multicollinearity problem , The model is well constructed . For the collinearity of variables ,VIF All less than 10, So the model has no multicollinearity problem , The model is well constructed .
The formula of the model is as follows ： RSR=-0.39+0.203*Probit

Output results 5： Fitting effect picture

Chart description ：  The figure above shows the original data of this model 、 Model fitting value 、 Model predictions .

Output results 6： Table of critical values for grading sorting

Chart description ： The purpose of this step is to get the table of critical values for grading sorting , In especial Probit The critical value corresponds to RSR critical value （ Fit value ）; First of all ： Percentile threshold and Probit The critical value varies according to the number of levels , These two terms are fixed values and correspond exactly to each other ; second ： In the table above RSR critical ( Fit value ) It's based on Probit The critical value is calculated by substituting it into the regression model .

Output results 7： Summary of grading results

Chart description ： Grading Level The larger the number, the higher the level , The better the effect . According to the three grades of the results in the above table , region D And regions F Of pregnant women do the best health care , And the region H Of pregnant women do the worst health care .

7、 matters needing attention

If in SPSSPRO Rank sum ratio test , It is hoped that each indicator has a weight （ If there is no weight, it is called RSR, Weighted is called WRSR,RSR yes WRSR Is a special form ）, You can select the variable weight on the input page “ Custom weights ” Set the variable weight at .

8、 Model theory

RSR The basic idea of law is : Rank the evaluation indexes , Take the average value of rank as the evaluation standard , It is applicable to the measurement of indicators in different measurement units Comprehensive evaluation of . RSR The basic steps of the method are :
step 1 Construct matrix ： Suppose the evaluation object is n individual , The evaluation index is m individual , Build data matrix (n ×m）.
step 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 , 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

（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 ：

For cost indicators ：

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

step 4 Calculate the unit of probability
Rank to get RSR( or WRSR) Frequency distribution table , List the frequency of each group f, Calculate the cumulative frequency of each group cf And cumulative frequency p, Convert to probability units probit.

step 5 Calculate the linear regression equation
With probit The value is an argument , With RSR As the dependent variable , Calculate the linear regression equation .

step 6 Grading sort , Calculated according to the regression equation RSR（WRSR） The evaluation objects are sorted according to the estimated value .

9、 reference

[1] Tianfengdiao . Rank sum ratio method and its application [M]. Beijing China Statistics Press ,1993.
[2] Liu Haoran , Tang Shaoliang . be based on TOPSIS Study on the equalization level of basic medical services in Jiangsu Province by rank sum ratio method and rank sum ratio method [J]. Chinese general practice ,2016,19(7):819-823. DOI:10.3969/j.issn.1007-9572.2016.07.017.

10、 Learning Websites

SPSSPRO- Free professional online data analysis platform

Edited on 11-26 16:26