censReg: Censored Regression (Tobit) Model

In censReg: Censored Regression (Tobit) Models

Censored Regression (Tobit) Model

Description

Fitting a model with a censored dependent variable.

Usage

censReg( formula, left = 0, right = Inf, data = sys.frame( sys.parent()),
   subset = NULL, start = NULL, nGHQ = 8, logLikOnly = FALSE, ... )

## S3 method for class 'censReg'
print( x, logSigma = TRUE, digits = 4, ... )

Arguments

formula	an object of class "formula": a symbolic description of the model to be fitted.
left	left limit for the censored dependent variable; if set to -Inf, the dependent variable is assumed to be not left-censored; defaults to zero (classical Tobit model).
right	right limit for the censored dependent variable; if set to Inf, the dependent variable is assumed to be not right-censored; defaults to Inf (classical Tobit model).
data	an optional data frame. If argument data is of class "pdata.frame", a panel-model is estimated.
subset	an optional vector specifying a subset of observations to be used in the fitting process.
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 start is not specified, initial values are taken from an OLS estimation or (uncensored) random-effects panel data estimation.
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 TRUE, the model is not estimated but the log-likelihood contributions of all observations/individuals and the corresponding gradients calculated at the parameters specified by argument start are returned.
x	object of class censReg (returned by censReg).
logSigma	logical value indicating whether the variance(s) of the model should be printed logarithmized (see coef.censReg).
digits	positive integer specifiying the minimum number of significant digits to be printed (see print.default).
...	additional arguments for censReg are passed to maxLik; additional arguments for print.censReg are currently ignored.

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

## 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 )

censReg documentation built on Sept. 9, 2022, 3:02 p.m.