Tobit Regression

Fitting and testing tobit regression models for censored data.

Usage

tobit(formula, left = 0, right = Inf, dist = "gaussian",
    subset = NULL, data = list(), ...)

Arguments

formula

a symbolic description of a regression model of type y ~ x1 + x2 + ....

left

left limit for the censored dependent variable y. If set to -Inf, y is assumed not to be left-censored. Can also be a vector of limits of the same length as y.

right

right limit for the censored dependent variable y. If set to Inf, the default, y is assumed not to be right-censored. Can also be a vector of limits of the same length as y.

dist

assumed distribution for the dependent variable y. This is passed to survreg, see the respective man page for more details.

subset

a specification of the rows to be used.

data

a data frame containing the variables in the model.

...

further arguments passed to survreg.

Details

The function tobit is a convenience interface to survreg (for survival regression, including censored regression) setting different defaults and providing a more convenient interface for specification of the censoring information.

The default is the classical tobit model (Tobin 1958, Greene 2003) assuming a normal distribution for the dependent variable with left-censoring at 0.

Technically, the formula of type y ~ x1 + x2 + ... passed to tobit is simply transformed into a formula suitable for survreg: This means the dependent variable is first censored and then wrapped into a Surv object containing the censoring information which is subsequently passed to survreg, e.g., Surv(ifelse(y <= 0, 0, y), y > 0, type = "left") ~ x1 + x2 + ... for the default settings.

References

Greene, W.H. (2003). Econometric Analysis, 5th edition. Upper Saddle River, NJ: Prentice Hall.

Tobin, J. (1958). Estimation of Relationships for Limited Dependent Variables. Econometrica, 26, 24–36.

Value

An object of class "tobit" inheriting from class "survreg".

Examples

data("Affairs")

## from Table 22.4 in Greene (2003)
fm.tobit <- tobit(affairs ~ age + yearsmarried + religiousness + occupation + rating,
  data = Affairs)
fm.tobit2 <- tobit(affairs ~ age + yearsmarried + religiousness + occupation + rating,
  right = 4, data = Affairs)

summary(fm.tobit)
#> 
#> Call:
#> tobit(formula = affairs ~ age + yearsmarried + religiousness + 
#>     occupation + rating, data = Affairs)
#> 
#> Observations:
#>          Total  Left-censored     Uncensored Right-censored 
#>            601            451            150              0 
#> 
#> Coefficients:
#>               Estimate Std. Error z value Pr(>|z|)    
#> (Intercept)    8.17420    2.74145   2.982  0.00287 ** 
#> age           -0.17933    0.07909  -2.267  0.02337 *  
#> yearsmarried   0.55414    0.13452   4.119 3.80e-05 ***
#> religiousness -1.68622    0.40375  -4.176 2.96e-05 ***
#> occupation     0.32605    0.25442   1.282  0.20001    
#> rating        -2.28497    0.40783  -5.603 2.11e-08 ***
#> Log(scale)     2.10986    0.06710  31.444  < 2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Scale: 8.247 
#> 
#> Gaussian distribution
#> Number of Newton-Raphson Iterations: 4 
#> Log-likelihood: -705.6 on 7 Df
#> Wald-statistic: 67.71 on 5 Df, p-value: 3.0718e-13 
#> 
summary(fm.tobit2)
#> 
#> Call:
#> tobit(formula = affairs ~ age + yearsmarried + religiousness + 
#>     occupation + rating, right = 4, data = Affairs)
#> 
#> Observations:
#>          Total  Left-censored     Uncensored Right-censored 
#>            601            451             70             80 
#> 
#> Coefficients:
#>               Estimate Std. Error z value Pr(>|z|)    
#> (Intercept)    7.90098    2.80385   2.818 0.004834 ** 
#> age           -0.17760    0.07991  -2.223 0.026244 *  
#> yearsmarried   0.53230    0.14117   3.771 0.000163 ***
#> religiousness -1.61634    0.42440  -3.809 0.000140 ***
#> occupation     0.32419    0.25388   1.277 0.201624    
#> rating        -2.20701    0.44983  -4.906 9.28e-07 ***
#> Log(scale)     2.07232    0.11040  18.772  < 2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Scale: 7.943 
#> 
#> Gaussian distribution
#> Number of Newton-Raphson Iterations: 4 
#> Log-likelihood:  -500 on 7 Df
#> Wald-statistic: 42.56 on 5 Df, p-value: 4.5387e-08 
#>