Censored Regression with Conditional Heteroscedasticy
Fitting censored (tobit) or truncated regression models with conditional heteroscedasticy.
crch(formula, data, subset, na.action, weights, offset,
link.scale = c("log", "identity", "quadratic"),
dist = c("gaussian", "logistic", "student"), df = NULL,
left = -Inf, right = Inf, truncated = FALSE,
type = c("ml", "crps"), control = crch.control(...),
model = TRUE, x = FALSE, y = FALSE, ...)
trch(formula, data, subset, na.action, weights, offset,
link.scale = c("log", "identity", "quadratic"),
dist = c("gaussian", "logistic", "student"), df = NULL,
left = -Inf, right = Inf, truncated = TRUE,
type = c("ml", "crps"), control = crch.control(...),
model = TRUE, x = FALSE, y = FALSE, ...)
crch.fit(x, z, y, left, right, truncated = FALSE, dist = "gaussian",
df = NULL, link.scale = "log", type = "ml", weights = NULL, offset = NULL,
control = crch.control())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 |
weights |
optional case weights in fitting. |
offset |
optional numeric vector with a priori known component to
be included in the linear predictor for the location. For |
link.scale |
character specification of the link function in
the scale model. Currently, |
dist |
assumed distribution for the dependent variable |
df |
optional degrees of freedom for |
left |
left limit for the censored dependent variable |
right |
right limit for the censored dependent variable |
truncated |
logical. If |
type |
loss function to be optimized. Can be either |
control |
a list of control parameters passed to |
model |
logical. If |
x, y |
for |
z |
a design matrix with regressors for the scale. |
... |
arguments to be used to form the default |
crch fits censored (tobit) or truncated regression models with conditional
heteroscedasticy with maximum likelihood estimation. Student-t, Gaussian, and
logistic distributions can be fitted to left- and/or right censored or
truncated responses. Different regressors can be used to model the location
and the scale of this distribution. If control=crch.boost()
optimization is performed by boosting.
trch is a wrapper function for crch with default
truncated = TRUE.
crch.fit is the lower level function where the actual
fitting takes place.
An object of class "crch" or "crch.boost", i.e., a list with the
following elements.
coefficients |
list of coefficients for location, scale, and df. Scale and df coefficients are in log-scale. |
df |
if |
residuals |
the residuals, that is response minus fitted values. |
fitted.values |
list of fitted location and scale parameters. |
dist |
assumed distribution for the dependent variable |
cens |
list of censoring points. |
optim |
output from optimization from |
method |
optimization method used for |
type |
used loss function (maximum likelihood or minimum CRPS). |
control |
list of control parameters passed to |
start |
starting values of coefficients used in the optimization. |
weights |
case weights used for fitting. |
offset |
list of offsets for location and scale. |
n |
number of observations. |
nobs |
number of observations with non-zero weights. |
loglik |
log-likelihood. |
vcov |
covariance matrix. |
link |
a list with element |
truncated |
logical indicating wheter a truncated model has been fitted. |
converged |
logical variable whether optimization has converged or not. |
iterations |
number of iterations in optimization. |
call |
function call. |
formula |
the formula supplied. |
terms |
the |
levels |
list of levels of the factors used in fitting for location and scale respectively. |
contrasts |
(where relevant) the contrasts used. |
y |
if requested, the response used. |
x |
if requested, the model matrix used. |
model |
if requested, the model frame used. |
stepsize, mstop, mstopopt, standardize |
return values of boosting
optimization. See |
Messner JW, Mayr GJ, Zeileis A (2016). Heteroscedastic Censored and Truncated Regression with crch. The R Journal, 3(1), 173–181. https://journal.R-project.org/archive/2016-1/messner-mayr-zeileis.pdf.
Messner JW, Zeileis A, Broecker J, Mayr GJ (2014). Probabilistic Wind Power Forecasts with an Inverse Power Curve Transformation and Censored Regression. Wind Energy, 17(11), 1753–1766. doi: 10.1002/we.1666.
data("RainIbk")
## mean and standard deviation of square root transformed ensemble forecasts
RainIbk$sqrtensmean <-
apply(sqrt(RainIbk[,grep('^rainfc',names(RainIbk))]), 1, mean)
RainIbk$sqrtenssd <-
apply(sqrt(RainIbk[,grep('^rainfc',names(RainIbk))]), 1, sd)
## fit linear regression model with Gaussian distribution
CRCH <- crch(sqrt(rain) ~ sqrtensmean, data = RainIbk, dist = "gaussian")
## same as lm?
all.equal(coef(lm(sqrt(rain) ~ sqrtensmean, data = RainIbk)),
head(coef(CRCH), -1), tolerance = .Machine$double.eps^0.25)
## print
CRCH
## summary
summary(CRCH)
## left censored regression model with censoring point 0:
CRCH2 <- crch(sqrt(rain) ~ sqrtensmean, data = RainIbk,
dist = "gaussian", left = 0)
## left censored regression model with censoring point 0 and
## conditional heteroscedasticy:
CRCH3 <- crch(sqrt(rain) ~ sqrtensmean|sqrtenssd, data = RainIbk,
dist = "gaussian", left = 0)
## left censored regression model with censoring point 0 and
## conditional heteroscedasticy with logistic distribution:
CRCH4 <- crch(sqrt(rain) ~ sqrtensmean|sqrtenssd, data = RainIbk,
dist = "logistic", left = 0)
## compare AIC
AIC(CRCH, CRCH2, CRCH3, CRCH4)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.