Description Usage Arguments Details Value References See Also Examples

Fitting tobit regression models with conditional heteroscedasticy.

1 2 3 4 5 6 7 |

`formula` |
a formula expression of the form |

`data` |
an optional data frame containing the variables occurring in the formulas. |

`subset` |
an optional vector specifying a subset of observations to be used for fitting. |

`na.action` |
a function which indicates what should happen when the data
contain |

`model` |
logical. If |

`x, y` |
for |

`z` |
a design matrix with regressors for the scale. |

`...` |
arguments to be used to form the default |

`control, maxit, start` |
a list of control parameters passed to |

`grad` |
logical. Should gradients be used for optimization? If |

`hessian` |
logical or character. Should a numeric approximation of the
(negative) Hessian matrix be computed? Either |

`htobit`

fits tobit regression models with conditional heteroscedasticy
using maximum likelihood estimation. The model assumes an underlying latent
Gaussian variable

*y* ~ N(mu, sigma^2)*

which is only observed if positive and zero otherwise: *y = max(0, y*)*.
The latent mean *mu* and scale *sigma* (latent standard deviation)
are linked to two different linear predictors

*mu = x'b*

*log(sigma) = z'g*

where the regressor vectors *x* and *z* can be set up without restrictions,
i.e., they can be identical, overlapping or completely different or just including an intercept, etc.

`htobit_fit`

is the lower level function where the actual fitting takes place.

A set of standard extractor functions for fitted model objects is available for
objects of class `"htobit"`

, including methods to the generic functions
`print`

, `summary`

, `coef`

,
`vcov`

, `logLik`

, `residuals`

,
`predict`

, `terms`

,
`model.frame`

, `model.matrix`

, `update`

,
`estfun`

and `bread`

(from the sandwich package),
`Boot`

(from the car package), and
`getSummary`

(from the memisc package, enabling `mtable`

).

See `predict.htobit`

and `coef.htobit`

for more details
on some methods with non-standard arguments.

This is a somewhat simpler reimplementation of `crch`

(Messner, Mayr, Zeileis 2016), illustrating how to create a package from
scratch. Compared to `crch`

, `htobit`

does not offer:
other response distributions beyond Gaussian, truncated rather than censored responses,
analytical Hessian, flexible link functions for the scale submodel, boosting rather than
full maximum likelihood estimation, among further features.

`htobit`

returns an object of class `"htobit"`

, i.e., a list with components as follows.
`htobit_fit`

returns an unclassed list with components up to `df`

.

`coefficients` |
a list with elements |

`counts` |
count of function and gradient evaluations from |

`convergence` |
convergence code from |

`message` |
optional further information from |

`vcov` |
covariance matrix of all parameters in the model, |

`residuals` |
a vector of raw residuals (observed - fitted), |

`fitted.values` |
a list with elements |

`method` |
the method argument passed to the |

`nobs` |
number of observations, |

`df` |
number of estimated parameters, |

`call` |
the original function call, |

`formula` |
the original formula, |

`terms` |
a list with elements |

`levels` |
a list with elements |

`contrasts` |
a list with elements |

`model` |
the full model frame (if |

`y` |
the numeric response vector (if |

`x` |
a list with elements |

Messner JW, Mayr GJ, Zeileis A (2016). Heteroscedastic Censored and
Truncated Regression with crch.
*The R Journal*, **8**(1), 173–181.
https://journal.R-project.org/archive/2016-1/messner-mayr-zeileis.pdf.

`crch`

, `predict.htobit`

, `coef.htobit`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
## data on alcohol and tobacco expenditures in Belgian households
data("AlcoholTobacco", package = "htobit2017")
AlcoholTobacco$persons <- with(AlcoholTobacco, adults + oldkids + youngkids)
## homoscedastic vs. heteroscedastic tobit model for budget share of alcohol
m0 <- htobit(alcohol ~ age + log(expenditure) + persons, data = AlcoholTobacco)
m1 <- update(m0, . ~ . | age + log(expenditure) + persons)
## comparison of the two models
AIC(m0, m1)
BIC(m0, m1)
if(require("lmtest")) {
lrtest(m0, m1)
}
## comparison with crch
if(require("crch")) {
c1 <- crch(alcohol ~ age + log(expenditure) + persons | age + log(expenditure) + persons,
data = AlcoholTobacco, left = 0)
cbind(coef(m1), coef(c1))
}
``` |

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