I start by doing a simple gaussian tobit by MLE:
x1 <- runif(1000) # E() = 0.5
x2 <- runif(1000)*2 # E() = 1
x3 <- runif(1000)*4 # E() = 2
ystar <- -7 + 4*x1 + 5*x2 + rnorm(1000) # is mean 0
y <- ystar
censored <- ystar <= 0
y[censored] <- 0
library(AER)
m <- tobit(y ~ x1 + x2, left=0, data=D)
summary(m)
Which gives:
Call:
tobit(formula = y ~ x1 + x2, left = 0, data = D)
Observations:
Total Left-censored Uncensored Right-censored
1000 500 500 0
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -7.19392 0.20772 -34.632 <2e-16 ***
x1 4.17418 0.15678 26.625 <2e-16 ***
x2 5.10423 0.11441 44.612 <2e-16 ***
Log(scale) 0.02672 0.03149 0.849 0.396
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1
Scale: 1.027
And we're doing fine; compared with the true paraemters of (-7,4,5,1)
we've recovered (-7.2, 4.2, 5.1, 1.03).
I now try to replicate this using crq():
yc <- rep(0,1000)
m <- crq(Curv(y, yc) ~ x1 + x2, tau=0.5, method="Pow", data=D)
This gives:
Coefficients:
[1] -7.154124 4.278266 5.051516
These numerical values look okay but:
> summary(m)
tau: [1] 0.5
Coefficients:
Value Std. Error t value Pr(>|t|)
(Intercept) -7.15412 0.00000 -Inf 0.00000
x1 4.27827 0.00000 Inf 0.00000
x2 5.05152 0.00000 Inf 0.00000
The standard errors are all 0.
What am I missing?
While I have your attention, could someone explain the `Surv()' object
to me? How would I use method="Por" and method="Pen" in
doing a
censored quantile regression?
--
Ajay Shah http://www.mayin.org/ajayshah
ajayshah at mayin.org
http://ajayshahblog.blogspot.com
<*(:-? - wizard who doesn't know the answer.
