Regression - logical regression

1、 effect

Logistic regression is a multivariable analysis method to study the relationship between binary dependent variable view and some influencing factors . But if the dependent variable is of multiple categories , Then we need to use multi classification logistic regression to study the relationship between dependent variables and some influencing factors .

2、 Input / output description

Input ： The dependent variable Y For classification variables , The independent variables X It is at least one quantitative variable or categorical variable .
Output ： The effect evaluation of logistic regression coefficient estimation and classification prediction .

3、 Case example

According to age 、 Monthly income 、 Gender 、 Family population and other influencing factors （ The independent variables ） To study the means of transportation for wage earners to and from work is bus and subway 、 Bicycle 、 Or a private car （ The dependent variable ）

4、 Modeling steps

For dichotomies ,
in consideration of    The values are continuous , So it cannot fit discrete variables . We can consider using it to fit the conditional probability   , Because the value of probability is continuous .
Ideally, the unit step function , But this step function is not differentiable , The logarithmic probability function is a commonly used alternative function ：

  The above formula can be converted into :

among , y As x The probability of a positive example , 1-y by x The probability of its counterexample . The ratio of the two is called probability （odds）. therefore , In fact, the value of dependent variable in logistic regression should be odds.
take y As a kind of posterior probability estimation , The rewriting formula has ：

  For multi classification logistic regression , By default, a certain class is compared with the remaining classes as a binary classification problem ,N There are three categories for N-1 Subcategory , obtain N-1 A binary model , Find out the corresponding probability of each two categories , The category with the highest probability is the prediction result of the new sample .