Tobit模型，具有白色标准误差的回归

Posted 2021-04-10

[地狱，有人可以告诉我如何在Tobit模型中使用White标准错误吗？以下代码适用于线性模型，但不适用于轨道模型。

library(censReg)
library(sandwich)

# OLS model 
reg_ols <- lm(vrs_eff ~ cows, data=milk_data)
summary(reg_ols)
# using White standard errors
# vcovHC: Heteroskedasticity-consistent estimation 
# of the covariance matrix of the coefficient estimates in regression models.
cov_mat_OLS <- vcovHC(reg_ols, type="HC")
cov_mat_OLS
# coeftest is a generic function for performing z and 
# (quasi-)t Wald tests of estimated coefficients.
# Calculate new t and p values with white standard errors
coeftest(reg_ols, cov_mat_OLS)

# Tobit model
reg_tobit <- censReg(vrs_eff ~ cows, left=0, right=1, data=milk_data)
summary(reg_tobit)
cov_mat_T <- vcovHC(reg_tobit, type="HC")
cov_mat_T
coeftest(reg_tobit, cov_mat_T)

summary(reg_ols)
summary(reg_tobit)

答案

[我们可以使用AER::tobit，该帮助页面告诉我们“功能tobit是survreg的便捷接口，”我们可以通过定义"Surv"对象来估算Tobit模型（这是很难的方法）。

无论如何，survreg()带来了robust=TRUE选项，以“使用健壮的“三明治”标准误差，如果公式中没有cluster（）项，则基于个体的独立性；如果存在集群​​，则基于聚类的独立性。“ robust=TRUE也通过AER::tobit()传递，因此它也与survreg()一起使用。

示范

首先，我们使自己相信，两种轨道方法都能得出相同的结果。

library(censReg); library(AER)
data("Affairs")

fit.censReg <- censReg(frml, data=Affairs, right=4)
fit.AER <- tobit(frml, data=Affairs, right=4, x=TRUE)
stopifnot(all.equal(fit.censReg$estimate[1:6], fit.AER$coefficients))

现在比较-首先没有明显的标准错误：

summary(tobit(frml, data=Affairs, right=4))$coefficients
# Test of coefficients:
#   
#                Estimate Std. Error z value  Pr(>|z|)    
# (Intercept)    7.900980   2.803855  2.8179 0.0048339 ** 
# age           -0.177598   0.079906 -2.2226 0.0262441 *  
# yearsmarried   0.532302   0.141168  3.7707 0.0001628 ***
# religiousness -1.616336   0.424397 -3.8085 0.0001398 ***
# occupation     0.324186   0.253878  1.2769 0.2016238    
# rating        -2.207007   0.449832 -4.9063 9.281e-07 ***
# Log(scale)     2.072319   0.110396 18.7717 < 2.2e-16 ***
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

第二，具有标准错误：

summary(tobit(frml, data=Affairs, right=4, robust=TRUE))$coefficients
# Test of coefficients:
#   
#               Estimate Std. Error z value  Pr(>|z|)    
# (Intercept)    7.90098    3.00928  2.6255 0.0086511 ** 
# age           -0.17760    0.08684 -2.0451 0.0408424 *  
# yearsmarried   0.53230    0.14457  3.6820 0.0002314 ***
# religiousness -1.61634    0.43674 -3.7009 0.0002148 ***
# occupation     0.32419    0.25338  1.2795 0.2007325    
# rating        -2.20701    0.44971 -4.9076 9.218e-07 ***
# Log(scale)     2.07232    0.11196 18.5088 < 2.2e-16 ***
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

但是请注意，sandwich::vcovCL()函数实际上是为群集设计的。但是我们可以稍微“破解”它，并以簇的形式给出个人观察，即行名。这适用于censReg()和tobit()：

library(sandwich)
coeftest(fit.AER, vcov.=vcovCL(fit.AER, cluster=rownames(Affairs), type="HC0"))
# z test of coefficients:
#   
#                Estimate Std. Error z value  Pr(>|z|)    
# (Intercept)    7.900980   3.011782  2.6234 0.0087068 ** 
# age           -0.177598   0.086912 -2.0434 0.0410105 *  
# yearsmarried   0.532302   0.144688  3.6790 0.0002342 ***
# religiousness -1.616336   0.437101 -3.6979 0.0002174 ***
# occupation     0.324186   0.253587  1.2784 0.2011075    
# rating        -2.207007   0.450084 -4.9035 9.412e-07 ***
# Log(scale)     2.072319   0.112057 18.4934 < 2.2e-16 ***
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

# same
coeftest(fit.censReg, vcov.=vcovCL(fit.censReg, cluster=rownames(Affairs), type="HC0"))

正如人们所看到的，vcovCL标准误差与AER::tobit(., robust=TRUE)基本上相同。