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Mathematical modeling: factor analysis
2022-07-05 08:36:00 【A little brother who studies mathematical modeling】
Catalog
1. What is factor analysis ?
Integrate the original indicators into new indicators ; Extract several common elements from many related variables , The aim is to simplify complex situations , With minimal information loss , Integrate many original indicators into a few comprehensive indicators , These comprehensive indicators are called factor analysis variables ( Not to delete indicators , It is a new indicator )
2. benefits
- Less factors , Analysis is simpler
- It is not a simple choice of the original variables , It's a reconstruction of the original variables , Most of the information that can reflect many original indicators , There will be no loss of key information
- Create new concepts , The concept factor can be extracted , Calculate the comprehensive score according to the weight, and then cluster
3. Formula presentation
Factor load
Equivalent to the regression coefficient , The greater the absolute value , The stronger the relationship between the common factor and the original variable
That's what we have here
Variable commonality
The degree to which all common factors explain the variable information , If the commonality of most variables is higher than 0.8, It shows that the extracted common factors have basically reflected the original variables 80% The above information
Calculation method :
Sum of squares of all factors
Variance contribution
factor F The ability to explain the total variance of all original variables , The higher the value , It shows that the higher the importance of this factor , It is an important indicator to measure public factors
Calculation method :
Sum of squares of factors
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