使用固定效果进行预测 [英] Prediction using Fixed Effects

问题描述

我有一个简单的数据集，为此我应用了一个简单的线性回归模型.现在，我想使用固定效果对模型进行更好的预测.我知道我也可以考虑创建虚拟变量，但是我的真实数据集包含更多的年份并且具有更多的变量，因此我想避免创建虚拟变量.

I have a simple data set for which I applied a simple linear regression model. Now I would like to use fixed effects to make a better prediction on the model. I know that I could also consider making dummy variables, but my real dataset consist of more years and has more variables so I would like to avoid making dummies.

我的数据和代码与此类似:

My data and code is similar to this:

data <- read.table(header = TRUE, 
                   stringsAsFactors = FALSE, 
                   text="CompanyNumber ResponseVariable Year ExplanatoryVariable1 ExplanatoryVariable2
                   1 2.5 2000 1 2
                   1 4 2001 3 1
                   1 3 2002 5 7
                   2 1 2000 3 2
                   2 2.4 2001 0 4
                   2 6 2002 2 9
                   3 10 2000 8 3")

library(lfe)
library(caret)
fe <- getfe(felm(data = data, ResponseVariable ~ ExplanatoryVariable1 + ExplanatoryVariable2 | Year))
fe
lm.1<-lm(ResponseVariable ~ ExplanatoryVariable1 + ExplanatoryVariable2, data=data)                                   


prediction<- predict(lm.1, data) 
prediction

check_model=postResample(pred = prediction, obs = data$ResponseVariable)
check_model

对于我的真实数据集，我将基于我的测试集进行预测，但为简单起见，我也只在这里使用训练集.

For my real dataset I will make a prediction based on my test set but for simplicity I just use the trainingset here as well.

我想借助我发现的固定效果做出预测.但这似乎与固定效果不匹配，任何知道如何使用此fe$effects的人?

I would like to make a prediction with the help of the fixed effects that I found. But it does not seem to match the fixed effect right, anyone who knows how to use this fe$effects?

prediction_fe<- predict(lm.1, data) + fe$effect

推荐答案

以下是有关您的设置和正在运行的模型的一些附加评论.

Here's a few extra comments on your setup and the models that you are running.

您适合的主要模型是

lm.1<-lm(ResponseVariable ~ ExplanatoryVariable1 + ExplanatoryVariable2, data=data) 

产生

> lm.1
Call:
lm(formula = ResponseVariable ~ ExplanatoryVariable1 + ExplanatoryVariable2, 
    data = data)

Coefficients:
         (Intercept)  ExplanatoryVariable1  ExplanatoryVariable2  
              0.8901                0.7857                0.1923  

在此模型上运行predict函数时，您会得到

When you run the predict function on this model you get

> predict(lm.1)
       1        2        3        4        5        6        7 
2.060385 3.439410 6.164590 3.631718 1.659333 4.192205 7.752359 

对应于计算(对于观察值1):0.8901 + 1 * 0.7857 + 2 * 0.1923，因此在预测中使用了估计的固定效果. felm模型稍微复杂些，因为它考虑"了年份成分.模型拟合显示在这里

That corresponds to computing (for observation 1) : 0.8901 + 1*0.7857 + 2*0.1923 so the estimated fixed effects are used in the prediction. The felm model is slightly more complicated as it "factors out" the year component. The model fit is shown here

> felm(data = data, ResponseVariable ~ ExplanatoryVariable1 + ExplanatoryVariable2 | Year)
ExplanatoryVariable1 ExplanatoryVariable2 
              0.9726               1.3262 

现在，这对应于Year的校正"或条件，因此如果适合，您将获得相同的结果

Now this correspond to "correcting for" or conditioning on Year so you get the same result if you fit

> lm(data = data, ResponseVariable ~ ExplanatoryVariable1 + ExplanatoryVariable2 + factor(Year))

Call:
lm(formula = ResponseVariable ~ ExplanatoryVariable1 + ExplanatoryVariable2 + 
    factor(Year), data = data)

Coefficients:
         (Intercept)  ExplanatoryVariable1  ExplanatoryVariable2      factor(Year)2001  
             -2.4848                0.9726                1.3262                0.9105  
    factor(Year)2002  
             -7.0286  

，然后只丢弃解释变量的所有系数.因此，您无法从felm提取的固定效果中获取预测(因为您缺少截距和全年的效果)，因此只能看到效果大小.

and then just throw away all but the coefficients for the explanatory variables. Thus, you cannnot go from the extracted fixed effects from felm and obtain the predictions (since you are lacking the intercept and all the year effects) - you can only see the effect sizes.

希望这会有所帮助.

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