Estimation of limited dependent variable models
mhurdle fits a large set of models relevant when the dependent variable is 0 for a part of the sample.
mhurdle(formula, data, subset, weights, na.action,
start = NULL,
dist = c("ln", "n", "bc", "ihs"),
h2 = FALSE,
scaled = TRUE,
corr = FALSE, robust = TRUE,
check.grad = FALSE, ...)
## S3 method for class 'mhurdle'
coef(object,
which = c("all", "h1", "h2", "h3", "h4", "sd", "corr", "tr", "pos"), ...)
## S3 method for class 'mhurdle'
vcov(object,
which = c("all", "h1", "h2", "h3", "h4", "sd", "corr", "tr", "pos"), ...)
## S3 method for class 'mhurdle'
logLik(object, naive = FALSE, ...)
## S3 method for class 'mhurdle'
print(x, digits = max(3, getOption("digits") - 2),
width = getOption("width"), ...)
## S3 method for class 'mhurdle'
summary(object, ...)
## S3 method for class 'summary.mhurdle'
print(x, digits = max(3, getOption("digits") - 2),
width = getOption("width"), ...)
## S3 method for class 'mhurdle'
fitted(object,
which = c("all", "zero", "positive"), ...)
## S3 method for class 'mhurdle'
predict(object, newdata = NULL, ...)
## S3 method for class 'mhurdle'
update(object, new, ...)formula |
a symbolic description of the model to be fitted, |
data |
a |
newdata |
a |
subset |
see |
weights |
see |
na.action |
see |
start |
starting values, |
dist |
the distribution of the error of the consumption equation:
one of |
h2 |
if |
scaled |
if |
corr |
a boolean indicating whether the errors of the different equations are correlated or not, |
robust |
transformation of the structural parameters in order to avoid numerical problems, |
check.grad |
if |
naive |
a boolean, it |
object,x |
an object of class |
new |
an updated formula for the |
digits |
see |
width |
see |
which |
which coefficients or covariances should be extracted ? Those of the
selection ( |
... |
further arguments. |
mhurdle fits models for which the dependent variable is zero for
a part of the sample. Null values of the dependent variable may occurs
because of one or several mechanisms : good rejection, lack of
ressources and purchase infrequency. The model is described using a
three-parts formula : the first part describes the selection process if
any, the second part the regression equation and the third part the
purchase infrequency process. y ~ 0 | x1 + x2 | z1 + z2 means
that there is no selection process. y ~ w1 + w2 | x1 + x2 | 0 and
y ~ w1 + w2 | x1 + x2 describe the same model with no purchase
infrequency process. The second part is mandatory, it explains the
positive values of the dependant variable. The dist argument
indicates the distribution of the error term. If dist = "n", the
error term is normal and (at least part of) the zero observations are
also explained by the second part as the result of a corner
solution. Several models described in the litterature are obtained as
special cases :
A model with a formula like y~0|x1+x2 and dist="n" is the
Tobit model proposed by Tobin (1958).
y~w1+w2|x1+x2 and dist="l" or dist="t" is the
single hurdle model proposed by Cragg (1971). With dist="n", the
double hurdle model also proposed by Cragg (1971) is obtained. With
corr="h1" we get the correlated version of this model described
by Blundell (1987).
y~0|x1+x2|z1+z2 is the P-Tobit model of Deaton and Irish (1984),
which can be a single hurdle model if dist="t" or dist="l"
or a double hurdle model if dist="n".
an object of class c("mhurdle", "maxLik").
A "mhurdle" object has the following elements :
the vector of coefficients,
the covariance matrix of the coefficients,
a matrix of fitted.values, the first column being the probability of 0 and the second one the mean values for the positive observations,
the log-likelihood,
the gradient at convergence,
a data.frame containing the variables used for the estimation,
a list containing the names of the coefficients in
the selection equation, the regression equation, the infrequency of
purchase equation and the other coefficients (the standard deviation
of the error term and the coefficient of correlation if corr = TRUE),
the model formula, an object of class Formula,
the call,
the lagrange multiplier test of no correlation.
Blundell R, Meghir C (1987). Bivariate Alternatives to the Tobit Model. Journal of Econometrics, 34, 179-200.
Cragg JG (1971). Some Statistical Models for Limited Dependent Variables with Applications for the Demand for Durable Goods. Econometrica, 39(5), 829-44.
Deaton A, Irish M (1984). A Statistical Model for Zero Expenditures in Household Budgets. Journal of Public Economics, 23, 59-80.
Tobin J (1958). Estimation of Relationships for Limited Dependent Variables. Econometrica, 26(1), 24-36.
data("Interview", package = "mhurdle")
# independent double hurdle model
idhm <- mhurdle(vacations ~ car + size | linc + linc2 | 0, Interview,
dist = "ln", h2 = TRUE, method = "bfgs")
# dependent double hurdle model
ddhm <- mhurdle(vacations ~ car + size | linc + linc2 | 0, Interview,
dist = "ln", h2 = TRUE, method = "bfgs", corr = TRUE)
# a double hurdle p-tobit model
ptm <- mhurdle(vacations ~ 0 | linc + linc2 | car + size, Interview,
dist = "ln", h2 = TRUE, method = "bfgs", corr = TRUE)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.