Confidence intervals for the coefficients of a Tobit model

Question

Given a linear regression model for a dependent variable that is left-censored at 0 (i.e., a Tobit model), how can I calculate confidence intervals for the coefficients?

Ideally, you would provide code for use with the R package censReg, but I ought to be able to implement an algorithm myself given a clear description.

(N.B. The similarly titled question "Confidence intervals for Tobit model in package AER in R" is actually about prediction intervals for the dependent variable, not confidence intervals for the coefficients.)

JimB · Accepted Answer · 2018-04-03T20:02:52.783

2

Using the example from censReg:

# Run analysis
  library(censReg)
  data( "Affairs", package = "AER" )
  estResult <- censReg( affairs ~ age + yearsmarried + religiousness +
    occupation + rating, data = Affairs )

# Standard errors
  se <- diag(-solve(estResult$hessian))^0.5

# Data frame with confidence intervals
  clTable <- data.frame(Estimates=estResult$estimate,
    lowerCL = estResult$estimate - 1.96*se,
    upperCL = estResult$estimate + 1.96*se)
  clTable

               Estimates    lowerCL     upperCL
(Intercept)    8.1741974  2.8009641 13.54743072
age           -0.1793326 -0.3343553 -0.02430983
yearsmarried   0.5541418  0.2904867  0.81779697
religiousness -1.6862205 -2.4775735 -0.89486745
occupation     0.3260532 -0.1726193  0.82472575
rating        -2.2849727 -3.0843154 -1.48563000

edited Apr 03 '18 at 20:02

answered Apr 03 '18 at 18:08

JimB

2,043
8
14

2

The first-principles approach is commendable, but I think you can just `confint(estResult, level=0.95)`. – dimitriy Apr 03 '18 at 18:47
@DimitriyV.Masterov Can't beat that! (+1) – JimB Apr 03 '18 at 19:15
You answered my question as I wrote it, but is there an approach that's correct for finite samples, as opposed to this asymptotic method? – Kodiologist Apr 03 '18 at 19:54
Kodiologist: You might want to change your mind about accepting my answer. Your edit inserted the more elegant and succinct code of @DimitriyV.Masterov and I can't take apparent credit for that. – JimB Apr 03 '18 at 20:04
Take credit, by all means. – dimitriy Apr 03 '18 at 20:35
1

@Kodiologist The usual solution to asymptotic approximation is to use the bootstrap. – dimitriy Apr 03 '18 at 23:14

Confidence intervals for the coefficients of a Tobit model

1 Answers1