R: Estimation of limited dependent variable models
mhurdle
R Documentation
Estimation of limited dependent variable models
Description
mhurdle fits a large set of models relevant when the dependent
variable is 0 for a part of the sample.
Usage
mhurdle(formula, data, subset, weights, na.action,
start = NULL,
dist = c("ln","tn","n", "bc", "ihs"),
corr = NULL, ...)
## S3 method for class 'mhurdle'
coef(object,
which = c("all", "h1", "h2", "h3", "sd", "corr", "tr"), ...)
## S3 method for class 'mhurdle'
vcov(object,
which = c("all", "h1", "h2", "h3", "sd", "corr", "tr"), ...)
## 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, ...)
Arguments
formula
a symbolic description of the model to be fitted,
data
a data.frame,
newdata
a data.frame for which the predictions should be computed,
subset
see lm,
weights
see lm,
na.action
see lm,
start
starting values,
dist
the distribution of the error of the consumption
equation: one of "n" (normal), "l" (log-normal) or "t" (truncated
normal),
corr
indicates whether the errors of the different equations
are correlated. For models with two equations, this can be either
"d" for dependent and "i" for independent. For models
with three equations, this should be a character of length three
containing values of "i" and "d",
naive
a boolean, it TRUE, the likelihood of the naive
model is returned,
object,x
an object of class "mhurdle",
new
an updated formula for the update method,
digits
see print,
width
see print,
which
which coefficients or covariances should be extracted ? Those of the
selection ("h1"), consumption ("h2") or purchase
("h3") equation, the other coefficients "other" (the
standard error and the coefficient of corr), the standard error
("sigma") or the coefficient of correlation ("rho"),
...
further arguments.
Details
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".
Value
an object of class c("mhurdle", "maxLik").
A "mhurdle" object has the following elements :
coefficients
the vector of coefficients,
vcov
the covariance matrix of the coefficients,
fitted.values
a matrix of fitted.values, the first column being
the probability of 0 and the second one the mean values for the
positive observations,
logLik
the log-likelihood,
gradient
the gradient at convergence,
model
a data.frame containing the variables used for the
estimation,
coef.names
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),
formula
the model formula, an object of class Formula,
call
the call,
rho
the lagrange multiplier test of no correlation.
References
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.
Examples
data("tobin", package = "survival")
# tobit model
model010 <- mhurdle(durable ~ 0 | age + quant | 0, tobin, dist = "n")
# independent double hurdle model
model110i <- mhurdle(durable ~ age | quant | 0, tobin, dist = "n")
# Cragg log-normal single hurdle model
model100il <- mhurdle(durable ~ age | quant | 0, tobin, dist = "ln")
# Cragg truncated-normal single hurdle model
model100it <- update(model100il, dist = "tn")
# a double-hurdle p-tobit
model011i <- mhurdle(durable ~ 0 | quant | age, tobin, dist = "n")
providing 
.