What model is good for the analysis of influencing factors?

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Here it is , With 【 Solve the main factors affecting coal prices 】 For example , Briefly introduce the models that can be used in the analysis of influencing factors .
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Analysis method of influencing factors of mathematical modeling ：
One 、PCA Principal component analysis
Principal component analysis (Principal Component Analysis), It is one of the most widely used data dimensionality reduction algorithms . In practical application, this algorithm can combine multiple influencing factors into fewer influencing factors .

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for example , Suppose the price f ( x ) ,f ( x ) Is caused by x 1 x_{1} x1​、 x 2 x_{2} x2​、 x 3 x_{3} x3​ Affected by . Now for price f ( x ) f(x) f(x) The influencing factors are 3 individual .
The data dimensionality reduction of principal component analysis , Can reduce the price f ( x ) f(x) f(x) The number of influencing factors .
Suppose that after using principal component analysis , Two influencing factors are obtained y 1 y_{1} y1​、 y 2 y_{2} y2​, Then the price can be determined f ( x ) f(x) f(x) suffer y 1 y_{1} y1​、 y 2 y_{2} y2​ Affected by , among y 1 = λ 1 x 1 + λ 2 x 2 + λ 3 x 3 y_{1}=\lambda_{1}x_{1}+\lambda_{2}x_{2}+\lambda_{3}x_{3} y1​=λ1​x1​+λ2​x2​+λ3​x3​、 y 2 = μ 1 x 1 + μ 2 x 2 + μ 3 x 3 y_{2}=\mu_{1}x_{1}+\mu_{2}x_{2}+\mu_{3}x_{3} y2​=μ1​x1​+μ2​x2​+μ3​x3​, λ \lambda λ and μ \mu μ Is the influencing factor x x x The coefficient of .

Therefore, through principal component analysis , We can get new and less influencing factors , And it can also reduce the fluctuation of individual influencing factors and the impact caused by noise , In addition, we get the correlation of the original influencing factors , It is also convenient for later data processing and analysis .

Besides , If you want to use this method , What is needed is the dependent variable （ The principal components , That is, the price in the above example ） And independent variables （ That is, different influencing factors ） Quantitative data .

Two 、 Grey correlation analysis
The grey correlation analysis method is based on the degree of similarity or dissimilarity of the development trend between factors , As a way to measure the degree of correlation between factors .

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What can be obtained by grey correlation analysis is , Similar relationship among various factors （ Specific relevance ）. This analytical method can be understood as , Take two factors over time （ Or other changes ） The curve of change is drawn on the line chart , Compare the similarity of changes between the two factors , And give the specific relevance . use
This method , Take the price in the previous example f ( x ) f(x) f(x) With influencing factors x 1 x_{1} x1​、 x 2 x_{2} x2​、 x 3 x_{3} x3​ Carry out grey correlation analysis between , You can get three correlation degrees , It reflects the similarity or dissimilarity of influencing factors and price changes respectively , The greater the numerical , It can be explained that the greater the degree of Correlation , conversely , Less relevant .
Grey correlation analysis and PCA The analytical method is the same , Specific quantitative data are required . But it seems that there is no professional software to carry out , However, there are many codes implemented in different languages on the Internet , You can search for .

3、 ... and 、AHP Analytic hierarchy process
Analytic hierarchy process (Analytic Hierarchy Process) It is a decision analysis method combining qualitative and quantitative methods to solve multi-objective complex problems .
To put it simply, it is about quantifiable relationships （ For example, the price of apple is twice that of watermelon ） Experience with decision makers （ If you think price is more important than quality control ） Combination , An analytical method to make decisions .

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The key step of analytic hierarchy process is , Compare the importance of different influencing factors in pairs , And give specific quantitative relationship out of objective or subjective ; Then put different plans , Compare the influence degree of different influencing factors , Specific quantitative relationships are also given out of objective or subjective factors . Then the optimal solution can be obtained through calculation .
So it can be interpreted as , This analysis method should be used in , Get the best solution from a variety of alternatives , It is not a method to get the main influencing factors and their relevance . But this method can avoid the problem that many factors cannot be well quantified , Combine the idea of this method with other analytical methods , It can realize the analysis of factors that cannot be quantified .

Four 、 Summary
in general , The three analysis methods have different preferences . Principal component analysis tends to simplify the influencing factors , So as to achieve the effect of optimization calculation ; Grey correlation analysis is a method to get the correlation degree between different factors . Both methods require specific quantitative data to be analyzed . Different from these two , Analytic hierarchy process is an analytical method for making excellent decisions , And it can realize the effect of quantifying subjective factors , Combining it with other methods can achieve better analysis .

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