Mathematical modeling: factor analysis

Catalog

1. What is factor analysis ？

2. benefits

3. Formula presentation

Factor load

Variable commonality

Variance contribution

---

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