MBnegbin: mboost Families for Binary, (Zero-Truncated) Negative...

In countreg: Count Data Regression

mboost Families for Binary, (Zero-Truncated) Negative Binomial and Zero-Truncated Poisson Regression

Description

Family generators for model-based boosting of count data regressions using mboost.

Usage

MBbinomial(link = "logit")

MBnegbin(theta = NULL, link = "log",
  control = list(reltol = .Machine$double.eps^(1/1.5), maxit = 500))

MBztpoisson(link = "log",
  control = list(reltol = .Machine$double.eps^(1/1.5), maxit = 500))

MBztnegbin(theta = NULL, link = "log",
  control = list(reltol = .Machine$double.eps^(1/1.5), maxit = 500))

Arguments

link	character or object of class "link-glm" for the link function linking the expectation and the predictor.
theta	numeric or NULL. Value of the theta parameter of the negative binomial model. If NULL, theta is estimated along with the regression coefficients.
control	list with control parameters passed to optim.

Details

The family generators MBbinomial, MBnegbin, MBztpoisson, MBztnegbin enable boosting of binary regressions, negative binomial count regressions, zero-truncated Poisson count regressions, and zero-truncated negative binomial count regressions, respectively. Family MBbinomial is comparable to Binomial but supports any link function (not just logit and probit). Family MBnegbin is comparable to NBinomial but is typically much faster because the nuisance parameter theta is estimated using analytical gradients (via optim) and setting better starting values. MBztpoisson and MBztnegbin enable zero-truncated Poisson and negative binomial regressions so that also the count parts of hurdle models can be easily estimated.

Value

An object of class boost_family_glm.

See Also

mboost, glmboost, gamboost, Binomial, Poisson, NBinomial

Examples

### Negative binomial regression for CrabSatellites ----------------------------

if(require("mboost")) {
## crab satellite data using ordered factors as numeric
data("CrabSatellites", package = "countreg")
CrabSatellites <- transform(CrabSatellites,
  color = as.numeric(color),
  spine = as.numeric(spine)
)  

## comparison of ML and boosting with NBinomial() vs. MBnegbin()
system.time(m0 <- glm.nb(satellites ~ width + color, data = CrabSatellites))
system.time(m1 <- glmboost(satellites ~ width + color, data = CrabSatellites,
  family = NBinomial(), control = boost_control(mstop = 500)))
system.time(m2 <- glmboost(satellites ~ width + color, data = CrabSatellites,
  family = MBnegbin(), control = boost_control(mstop = 500)))
## note that mstop is _not_ tuned here to (ab)use mboost to get the ML estimator

## compare coefficients
cbind(c(coef(m0), "theta" = m0$theta),
  c(coef(m1, off2int = TRUE, which = ""), nuisance(m1)),
  c(coef(m1, off2int = TRUE, which = ""), nuisance(m1))
)
}

### Hurdle regression for CrabSatellites using spline terms --------------------


if(require("mboost")) {
## ML estimation
g <- hurdle(satellites ~ width + color, data = CrabSatellites, dist = "negbin")
summary(g)

## boosting of zero hurdle
g0 <- gamboost(factor(satellites > 0) ~ bbs(width) + bbs(color, knots = 3),
  data = CrabSatellites, family = MBbinomial())
set.seed(0)
g0cv <- cvrisk(g0)
g0[mstop(g0cv)]

## boosting of count regression
g1 <- gamboost(satellites ~ bbs(width) + bbs(color, knots = 3),
  data = subset(CrabSatellites, satellites > 0), family = MBztnegbin())
set.seed(1)
g1cv <- cvrisk(g1)
g1[mstop(g1cv)]

par(mfrow = c(1, 2))

## optimal mstop values
plot(g0cv)
plot(g1cv)
## -> no effects in covariates for count part

## partial effects in zero hurdle
plot(g0)
## -> large effect of width, moderate effect of color with
## width effect almost linear
}


### Hurdle regression for RecreationDemand using linear terms ------------------

## Not run: 
library("mboost")
data("RecreationDemand", package = "AER")

### Zero hurdle ##

## ML vs. boosting
z0 <- glm(factor(trips > 0) ~ ., data = RecreationDemand, family = binomial)
z1 <- glmboost(factor(trips > 0) ~ ., data = RecreationDemand, family = MBbinomial(),
  control = boost_control(mstop = 5000))
plot(z1)

## tune mstop
set.seed(0)
z1cv <- cvrisk(z1)
z1cv
plot(z1cv)
## very flat (presumably due to separation?)
## -> stop earlier manually
z1[3000]

## compare coefficients
cbind(coef(z0), coef(z1, off2int = TRUE, which = ""))
## -> some shrunken entirely to zero,
## coefficient of variable with separation (userfee) shrunken considerably


### Count (zero-truncated)

## ML and boosting count part
c0 <- zerotrunc(trips ~ ., data = subset(RecreationDemand, trips > 0), dist = "negbin")
c1 <- glmboost(trips ~ ., data = subset(RecreationDemand, trips > 0),
  family = MBztnegbin(), control = boost_control(mstop = 5000))
plot(c1)

## tune mstop
set.seed(0)
c1cv <- cvrisk(c1)
c1cv
plot(c1cv)

## use mstop from cvrisk
c1[mstop(c1cv)]

## compare coefficients
cbind(c(coef(c0), "theta" = c0$theta),
  c(coef(c1, off2int = TRUE, which = ""), nuisance(c1)))
## -> similar

## End(Not run)

countreg documentation built on Dec. 4, 2023, 3:09 a.m.