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crch.boost

Auxiliary functions to fit crch models via boosting.

Description

Auxiliary functions to fit crch models via boosting

Usage

crch.boost(maxit = 100, nu = 0.1, start = NULL, dot = "separate", 
  mstop = c("max", "aic", "bic", "cv"),  nfolds = 10, foldid = NULL, 
  maxvar = NULL)

crch.boost.fit(x, z, y, left, right, truncated = FALSE, dist = "gaussian",
  df = NULL, link.scale = "log", type = "ml", weights = NULL, offset = NULL, 
  control = crch.boost())

Arguments

maxit

the maximum number of boosting iterations.
nu

boosting step size. Default is 0.1.
start

a previously boosted but not converged "crch.boost" object to continue.
dot

character specifying how to process formula parts with a dot (.) on the right-hand side. This can either be "separate" so that each formula part is expanded separately or "sequential" so that the parts are expanded sequentially conditional on all prior parts. Default is "separate"
mstop

method to find optimum stopping iteration. Default is "max" which is maxit. Alternatives are "aic" and "bic" for AIC and BIC optimization and "cv" for cross validation. mstop can also be a positive integer to set the number of boosting iterations. Then maxit is set to mstop and mstop="max".
nfolds

if mstopopt = "cv", number of folds in cross validation.
foldid

if mstopopt = "cv", an optional vector of values between 1 and nfold identifying the fold each observation is in. If supplied, nfolds can be missing.
maxvar

Positive numeric. Maximum number of parameters to be selected during each iteration (not including intercepts). Used for stability selection.
x, z, y, left, right, truncated, dist, df, link.scale, type, weights, offset, control

see crch.fit for details.

Details

crch.boost extends crch to fit censored (tobit) or truncated regression models with conditional heteroscedasticy by boosting. If crch.boost() is supplied as control in crch then crch.boost.fit is used as lower level fitting function. Note that crch.control() with method=boosting is equivalent to crch.boost(). Thus, boosting can more conveniently be called with crch(..., method = "boosting").

Value

For crch.boost: A list with components named as the arguments. For crch.boost.fit: An object of class "crch.boost", i.e., a list with the following elements.

coefficients

list of coefficients for location and scale. Scale coefficients are in log-scale. Coefficients are of optimum stopping stopping iteration specified by mstop.
df

if dist = "student": degrees of freedom of student-t distribution. else NULL.
residuals

the residuals, that is response minus fitted values.
fitted.values

list of fitted location and scale parameters at optimum stopping iteration specified by mstop.
dist

assumed distribution for the dependent variable y.
cens

list of censoring points.
control

list of control parameters.
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.
link

a list with element "scale" containing the link objects for the scale model.
truncated

logical indicating wheter a truncated model has been fitted.
iterations

number of boosting iterations.
stepsize

boosting stepsize nu.
mstop

criterion used to find optimum stopping iteration.
mstopopt

optimum stopping iterations for different criteria.
standardize

list of center and scale values used to standardize response and regressors.

References

Messner JW, Mayr GJ, Zeileis A (2017). Non-Homogeneous Boosting for Predictor Selection in Ensemble Post-Processing. Monthly Weather Review, 145(1), 137–147, doi: 10.1175/MWR-D-16-0088.1.

See Also

Examples

# generate data
suppressWarnings(RNGversion("3.5.0"))
set.seed(5)
x <- matrix(rnorm(1000*20),1000,20)
y <- rnorm(1000, 1 + x[,1] - 1.5 * x[,2], exp(-1 + 0.3*x[,3]))
y <- pmax(0, y)
data <- data.frame(cbind(y, x))

# fit model with maximum likelihood
CRCH <- crch(y ~ .|., data = data, dist = "gaussian", left = 0)

# fit model with boosting
boost <- crch(y ~ .|.,  data = data, dist = "gaussian", left = 0,
  control = crch.boost(mstop = "aic"))

# more conveniently, the same model can also be fit through
# boost <- crch(y ~ .|.,  data = data, dist = "gaussian", left = 0,
#   method = "boosting", mstop = "aic")

# AIC comparison
AIC(CRCH, boost)

# summary
summary(boost)

# plot
plot(boost)
crch

Censored Regression with Conditional Heteroscedasticity

v1.0-4
GPL-2 | GPL-3
Authors
Jakob Messner [aut, cre] (<https://orcid.org/0000-0002-1027-3673>), Achim Zeileis [aut] (<https://orcid.org/0000-0003-0918-3766>), Reto Stauffer [aut] (<https://orcid.org/0000-0002-3798-5507>)
Initial release
2019-08-19

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