从0开始学习R语言--Day54--双重固定模型

对于具有空间差异的数据，如果不知道数据的特征关系或意义，直接用杜宾模型来处理是一个比较通用的思路，只是后续还需要很多检验去证明结果的可解释性和统计性。

但如果我们已经知道特征的意义，比如企业经济发展的数据中有着员工的科研能力，公司文化，当下的政策改革，外界的经济变化，我们就可以将其分为个体效应（不随时间改变的特征）和时间效应（所有个体共同经历的时间趋势），从而能够快速直接地分析出各个地域企业的发展状况。

以下是一个例子：

# 加载必要的包
library(plm)
library(lmtest)
library(dplyr)

# 生成模拟数据集
set.seed(123)
n <- 100  # 个体数量
t <- 5    # 时间周期

# 创建面板数据结构
data <- expand.grid(id = 1:n, time = 1:t) %>%
  mutate(
    # 个体固定效应(不随时间变化)
    alpha_i = rnorm(n, mean = 0, sd = 2)[id],
    # 时间固定效应(不随个体变化)
    gamma_t = rnorm(t, mean = 0, sd = 1)[time],
    # 解释变量
    X = rnorm(n*t, mean = 5, sd = 2),
    # 误差项
    epsilon = rnorm(n*t, mean = 0, sd = 1),
    # 生成因变量(真实系数β=0.8)
    Y = 0.8 * X + alpha_i + gamma_t + epsilon
  )

# 查看前几行数据
head(data)

# 双重固定效应模型估计
twoway_model <- plm(Y ~ X, 
                    data = data, 
                    index = c("id", "time"), 
                    model = "within", 
                    effect = "twoways")

# 混合模型(无固定效应)
pooled_model <- plm(Y ~ X, 
                    data = data, 
                    index = c("id", "time"), 
                    model = "pooling")

# 个体固定效应模型
individual_model <- plm(Y ~ X, 
                        data = data, 
                        index = c("id", "time"), 
                        model = "within", 
                        effect = "individual")

# 时间固定效应模型
time_model <- plm(Y ~ X, 
                  data = data, 
                  index = c("id", "time"), 
                  model = "within", 
                  effect = "time")

# 查看双重固定效应模型结果
summary(twoway_model)

# 正确进行F检验的方法
# 1. 检验双重固定效应是否优于混合模型
pFtest(twoway_model, pooled_model)

# 2. 检验个体固定效应是否显著
pFtest(individual_model, pooled_model)

# 3. 检验时间固定效应是否显著
pFtest(time_model, pooled_model)

# 4. 检验双重固定效应是否优于仅个体固定效应
pFtest(twoway_model, individual_model)

# 5. 检验双重固定效应是否优于仅时间固定效应
pFtest(twoway_model, time_model)

输出：

Twoways effects Within Model

Call:
plm(formula = Y ~ X, data = data, effect = "twoways", model = "within", 
    index = c("id", "time"))

Balanced Panel: n = 100, T = 5, N = 500

Residuals:
     Min.   1st Qu.    Median   3rd Qu.      Max. 
-3.224723 -0.583125 -0.010202  0.599678  2.960869 

Coefficients:
  Estimate Std. Error t-value  Pr(>|t|)    
X 0.778466   0.026107  29.818 < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Total Sum of Squares:    1329.9
Residual Sum of Squares: 409.08
R-Squared:      0.6924
Adj. R-Squared: 0.61141
F-statistic: 889.127 on 1 and 395 DF, p-value: < 2.22e-16
	F test for twoways effects

data:  Y ~ X
F = 17.185, df1 = 103, df2 = 395, p-value < 2.2e-16
alternative hypothesis: significant effects
	F test for individual effects

data:  Y ~ X
F = 13.23, df1 = 99, df2 = 399, p-value < 2.2e-16
alternative hypothesis: significant effects
	F test for time effects

data:  Y ~ X
F = 6.673, df1 = 4, df2 = 494, p-value = 3.094e-05
alternative hypothesis: significant effects
	F test for twoways effects

data:  Y ~ X
F = 27.637, df1 = 4, df2 = 395, p-value < 2.2e-16
alternative hypothesis: significant effects
	F test for twoways effects

data:  Y ~ X
F = 16.759, df1 = 99, df2 = 395, p-value < 2.2e-16
alternative hypothesis: significant effects

输出表明：模型需要固定效应加入到模型中，且个体效应非常显著，只是需要控制个别特殊异体，时间效应同理；所有的F的p值都小于0.001，说明必须同时控制时间和个体固定效应，结果中X的系数为0.778，表明是纯净的因果效应，而标准差0.026则说明模型的精度较高。