hurdle {pscl} | R Documentation |
Fit hurdle regression models for count data via maximum likelihood.
hurdle(formula, data, subset, na.action, weights, offset, dist = c("poisson", "negbin", "geometric"), zero.dist = c("binomial", "poisson", "negbin", "geometric"), link = c("logit", "probit", "cloglog", "cauchit", "log"), control = hurdle.control(...), model = TRUE, y = TRUE, x = FALSE, ...)
formula |
symbolic description of the model, see details. |
data, subset, na.action |
arguments controlling formula processing
via model.frame . |
weights |
optional numeric vector of weights. |
offset |
optional numeric vector with an a priori known component to be included in the linear predictor of the count model. |
dist |
character specification of count model family. |
zero.dist |
character specification of the zero hurdle model family. |
link |
character specification of link function in the binomial
zero hurdle (only used if zero.dist = "binomial" . |
control |
a list of control arguments specified via
hurdle.control . |
model, y, x |
logicals. If TRUE the corresponding components
of the fit (model frame, response, model matrix) are returned. |
... |
arguments passed to hurdle.control in the
default setup. |
Hurdle count models are two-component models with a truncated count component for positive counts and a hurdle component that models the zero counts. Thus, unlike zero-inflation models, there are not two sources of zeros: the count model is only employed if the hurdle for modeling the occurence of zeros is exceeded. The count model is typically a truncated Poisson or negative binomial regression (with log link). The geometric distribution is a special case of the negative binomial with size parameter equal to 1. For modeling the hurdle (occurence of positive counts) either a binomial model can be employed or a censored count distribution. Binomial logit and censored geometric models as the hurdle part both lead to the same likelihood function and thus to the same coefficient estimates.
The formula
can be used to specify both components of the model:
If a formula
of type y ~ x1 + x2
is supplied, then the same
regressors are employed in both components. This is equivalent to
y ~ x1 + x2 | x1 + x2
. Of course, a different set of regressors
could be specified for the zero hurdle component, e.g.,
y ~ x1 + x2 | z1 + z2 + z3
giving the count data model y ~ x1 + x2
conditional on (|
) the zero hurdle model y ~ z1 + z2 + z3
.
All parameters are estimated by maximum likelihood using optim
,
with control options set in hurdle.control
.
Starting values can be supplied, otherwise they are estimated by glm.fit
(the default). By default, the two components of the model are estimated separately
using two optim
calls. Standard errors are derived numerically using
the Hessian matrix returned by optim
. See
hurdle.control
for details.
The returned fitted model object is of class "hurdle"
and is similar
to fitted "glm"
objects. For elements such as "coefficients"
or
"terms"
a list is returned with elements for the zero and count components,
respectively. For details see below.
A set of standard extractor functions for fitted model objects is available for
objects of class "hurdle"
, including methods to the generic functions
print
, summary
, coef
,
vcov
, logLik
, residuals
,
predict
, fitted
, terms
,
model.matrix
. See predict.hurdle
for more details
on all methods.
An object of class "hurdle"
, i.e., a list with components including
coefficients |
a list with elements "count" and "zero"
containing the coefficients from the respective models, |
residuals |
a vector of raw residuals (observed - fitted), |
fitted.values |
a vector of fitted means, |
optim |
a list (of lists) with the output(s) from the optim call(s) for
minimizing the negative log-likelihood(s), |
control |
the control arguments passed to the optim call, |
start |
the starting values for the parameters passed to the optim call(s), |
weights |
the case weights used, |
offset |
the offset vector used (if any), |
n |
number of observations, |
df.null |
residual degrees of freedom for the null model (= n - 2 ), |
df.residual |
residual degrees of freedom for fitted model, |
terms |
a list with elements "count" , "zero" and
"full" containing the terms objects for the respective models, |
theta |
estimate of the additional theta parameter of the negative binomial model(s) (if negative binomial component is used), |
SE.logtheta |
standard error(s) for log(theta), |
loglik |
log-likelihood of the fitted model, |
vcov |
covariance matrix of all coefficients in the model (derived from the
Hessian of the optim output(s)), |
dist |
a list with elements "count" and "zero" with character
strings describing the respective distributions used, |
link |
character string describing the link if a binomial zero hurdle model is used, |
linkinv |
the inverse link function corresponding to link , |
converged |
logical indicating successful convergence of optim , |
call |
the original function call, |
formula |
the original formula, |
levels |
levels of the categorical regressors, |
contrasts |
a list with elements "count" and "zero"
containing the contrasts corresponding to levels from the
respective models, |
model |
the full model frame (if model = TRUE ), |
y |
the response count vector (if y = TRUE ), |
x |
a list with elements "count" and "zero"
containing the model matrices from the respective models
(if x = TRUE ). |
Achim Zeileis <Achim.Zeileis@R-project.org>
Cameron, A. Colin and Pravin K. Trivedi. 1998. Regression Analysis of Count Data. New York: Cambridge University Press.
Cameron, A. Colin and Pravin K. Trivedi 2005. Microeconometrics: Methods and Applications. Cambridge: Cambridge University Press.
Mullahy, J. 1986. Specification and Testing of Some Modified Count Data Models. Journal of Econometrics. 33:341–365.
Zeileis, Achim, Christian Kleiber and Simon Jackman 2008. “Regression Models for Count Data in R.” Journal of Statistical Software, 27(8). URL http://www.jstatsoft.org/v27/i08/.
hurdle.control
, glm
,
glm.fit
, glm.nb
,
zeroinfl
## data data("bioChemists", package = "pscl") ## logit-poisson ## "art ~ ." is the same as "art ~ . | .", i.e. ## "art ~ fem + mar + kid5 + phd + ment | fem + mar + kid5 + phd + ment" fm_hp1 <- hurdle(art ~ ., data = bioChemists) summary(fm_hp1) ## geometric-poisson fm_hp2 <- hurdle(art ~ ., data = bioChemists, zero = "geometric") summary(fm_hp2) ## logit and geometric model are equivalent coef(fm_hp1, model = "zero") - coef(fm_hp2, model = "zero") ## logit-negbin fm_hnb1 <- hurdle(art ~ ., data = bioChemists, dist = "negbin") summary(fm_hnb1) ## negbin-negbin fm_hnb2 <- hurdle(art ~ ., data = bioChemists, dist = "negbin", zero = "negbin") summary(fm_hnb2)