Question

地狱，有人能告诉我如何在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)

Answer 1

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{{1} }对象（这是很难的方法）。

无论如何，"Surv"为{em>带来了survreg()选项：“如果公式中没有cluster（）项，则基于个人的独立性，使用健壮的'三明治'标准误差，基于并且robust=TRUE也可以与robust=TRUE一起使用，因为它会传递给AER::tobit()。

演示

首先，我们使自己确信，两种轨道方法都能得出相同的结果。

survreg()

现在比较-首先没有明显的标准错误：

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))

第二，具有可靠的标准错误：

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

请注意，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函数实际上是为集群设计的。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。这对sandwich::vcovCL()和censReg()都适用：

tobit()

可以看到，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"))标准错误与vcovCL基本上相同。

Tobit模型，具有白色标准误差的回归

1 个答案:

演示