# Censored Regression (Tobit) Model

### Description

Fitting a model with a censored dependent variable.

### Usage

1 2 3 4 5 |

### Arguments

`formula` |
an object of class |

`left` |
left limit for the censored dependent variable;
if set to |

`right` |
right limit for the censored dependent variable;
if set to |

`data` |
an optional data frame.
If argument |

`start` |
an optional vector of initial parameters for the ML estimation
(intercept, slope parameters, logarithm of the standard deviation
of the individual effects (only for random-effects panel data models),
and logarithm of the standard deviation of the general disturbance term);
if |

`nGHQ` |
number of points used in the Gauss-Hermite quadrature, which is used to compute the log-likelihood value in case of the random effects model for panel data. |

`logLikOnly` |
logical. If |

`x` |
object of class |

`logSigma` |
logical value indicating whether the variance(s)
of the model should be printed logarithmized
(see |

`digits` |
positive integer specifiying the minimum number of
significant digits to be printed
(see |

`...` |
additional arguments for |

### Details

The model is estimated by Maximum Likelihood (ML)
assuming a Gaussian (normal) distribution of the error term.
The maximization of the likelihood function is done
by function `maxLik`

of the maxLik package.
An additional argument `method`

can be used to specify
the optimization method used by `maxLik`

,
e.g.\ `"Newton-Raphson"`

, `"BHHH"`

, `"BFGS"`

,
`"SANN"`

(for simulated annealing), or
`"NM"`

(for Nelder-Mead).

### Value

If argument `logLikOnly`

is `FALSE`

(default),
`censReg`

returns an object of class `"censReg"`

inheriting from class `"maxLik"`

.
The returned object contains the same components as objects
returned by `maxLik`

and additionally
the following components:

`call` |
the matched call. |

`terms` |
the model terms. |

`nObs` |
a vector containing 4 integer values: the total number of observations, the number of left-censored observations, the number of uncensored observations, and the number of right-censored observations. |

`df.residual` |
degrees of freedom of the residuals. |

`start` |
vector of starting values. |

`left` |
left limit of the censored dependent variable. |

`right` |
right limit of the censored dependent variable. |

`xMean` |
vector of mean values of the explanatory variables. |

In contrast,
if argument `logLikOnly`

is `TRUE`

,
`censReg`

returns a vector
of the log-likelihood contributions of all observations/individuals.
This vector has an attribute `"gradient"`

,
which is a matrix containing the gradients of the log-likelihood contributions
with respect to the parameters.

### Note

When the censored regression model is estimated,
the log-likelihood function is maximized with respect
to the coefficients and the *logarithm(s)*
of the variance(s).

### Author(s)

Arne Henningsen

### References

Greene, W.H. (2008):
*Econometric Analysis*, Sixth Edition, Prentice Hall, p. 871-875.

Kleiber, C. and Zeileis, A. (2008):
*Applied Econometrics with R*, Springer, p. 141-143.

Tobin, J. (1958):
Estimation of Relationships for Limited Dependent Variables.
*Econometrica* 26, p. 24-36.

### See Also

`summary.censReg`

, `coef.censReg`

,
`tobit`

, `selection`

### Examples

1 2 3 4 5 6 7 8 9 10 | ```
## Kleiber & Zeileis ( 2008 ), page 142
data( "Affairs", package = "AER" )
estResult <- censReg( affairs ~ age + yearsmarried + religiousness +
occupation + rating, data = Affairs )
print( estResult )
## Kleiber & Zeileis ( 2008 ), page 143
estResultBoth <- censReg( affairs ~ age + yearsmarried + religiousness +
occupation + rating, data = Affairs, right = 4 )
print( estResultBoth )
``` |

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