PSM summary

background

When evaluating the experimental effect , In a nonrandom experiment , Correlation is not causality , There are various deviations .

• example 1： Conduct a survey , The content of the survey is whether going to the hospital or not will affect personal health , Therefore, questionnaires were sent to all kinds of personnel in the hospital and their health status was obtained , Finally, I found that going to the hospital was bad for my health .

  Sample selection bias ：sample selection bias

• example 2： Evaluate the effectiveness of a pollution control policy , Select the area with basically the same pollution degree at the beginning of the period as the sample , And decide whether to implement the policy according to the wishes of each region ,3 After the year, the pollution index of the places where the policy is implemented is significantly lower than that of the areas where the policy is not implemented , The conclusion is that this policy is effective .

  Self selection bias ：self-selection bias： Whether the policies implemented by each region have been included in the interference item , Related to explanatory variables , Cause endogenesis

Experimental ATT And ATE

ATT：average treatment effect on the treated
Randomized trials ： Find the subject “ Parallel time and space ”

Hard to find in reality “ Parallel time and space ”, Only the difference between the subject and the non subject can be calculated

ATE：average treatment effect

Let the selection deviation be 0 -> Conditional expectation equals expectation ,D And y Independence between -> Control impact D Factors , Whether or not an individual participates in the experiment is “ Random ” Of

D And y Independence between ：CIA hypothesis

summary

• It is estimated that ATT The best way is to find the self of the individual participating in the experiment in parallel time and space , And assume that the parallel spacetime self did not participate in the experiment , Finally, the purest ATT, But it is unrealistic to find yourself in parallel time and space ;
• Second best , We can use randomly divided treatment groups and control groups , Make a difference and get ATT, But in reality, the choice of whether an individual participates in the experiment is not random ;
• In order to get a sample of randomized grouping , Find out the factors that affect whether an individual participates in the experiment , Control the equal value of factors between the two groups , Finally, the processed grouped samples are used to make a difference to get ATT.

PSM

The essence ： Match individuals with similar probability of participating in the experiment , Make the experiment approximate to a random experiment .

The key ： Find the variables that affect individual participation in the experiment .

Existing problems ： Variable unobservable ; Variables are observable , But high dimension , Resulting in sparse data -> Use propensity scores , It is equivalent to reducing the dimension of multiple confounding variables to a fraction .

Propensity score calculation

The dependent variable ： Whether to accept the experiment $D=1$
The independent variables ： At the same time influence D And y Characteristics of （CIA Suppose it is true ）
Model ： A dichotomous model
Positive sample 、 Negative sample selection ：treatment Whether it is an active choice ？

Predicted by negative samples prediction_score Isn't it because our model is not accurate ？
—— Co support hypothesis

Pairing method

Nearest neighbor matching ： Choose the one with the closest score ; It can be divided into with and without return .

PSM And DID

At the moment t Exert influence , Two ways to calculate the effect ：

• Affected people t After the performance - Unaffected people t After the performance
• Affected people t after performance - Affected people t front performance

PSM Eliminate the differences between people in the first idea , and DID combination , It is equivalent to introducing the second time dimension , Further match the crowd , The combination of the two is better .

reference

https://zhuanlan.zhihu.com/p/392443329