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\name{anova.lmrob}
\alias{anova.lmrob}
\title{Analysis of Robust Deviances ('anova') for "lmrob" Objects}
\description{
Compute an analysis of robust Wald-type or deviance-type test tables
for one or more linear regression models fitted by \code{\link{lmrob}}.
}
\usage{
\method{anova}{lmrob}(object, \dots, test = c("Wald", "Deviance"),
verbose = getOption("verbose"))
}
\arguments{
\item{object, \dots}{objects of class \code{"lmrob"}, typically
the result of a call to \code{\link{lmrob}}. \code{\dots} arguments
may also be symbolic descriptions of the reduced models
(cf. argument \code{formula} in \code{\link{lm}}).
}
\item{test}{a character string specifying the test statistic to be used.
Can be one of \code{"Wald"} or \code{"Deviance"},
with partial matching allowed, for specifying a \code{"Wald"}-type
test or \code{"Deviance"}-type test.}
\item{verbose}{logical; if true some informative messages are printed.}
}
\details{
Specifying a single object gives a sequential analysis of a robust
quasi-deviance table for that fit. That is, the reductions in the
robust residual deviance as each term of the formula is added in turn
are given in as the rows of a table. (Currently not yet implemented.)
If more than one object is specified, the table has a row for the
residual quasi-degrees of freedom (however, this information is never
used in the asymptotic tests). For all but the first model, the
change in degrees of freedom and robust deviance is also given. (This
only makes statistical sense if the models are nested.) As opposed to
the convention, the models are forced to be listed from largest to
smallest due to computational reasons.
In addition, the table will contain test statistics and P values
comparing the reduction in robust deviances for the model on the row
to that on top of it. There are two different robust tests available:
The "Wald"-type test (\code{test = "Wald"}) and the Deviance-type test
(\code{test = "Deviance"}). When using formula description of the
nested models in the dot arguments and \code{test = "Deviance"}, you
may be urged to supply a \code{\link{lmrob}} fit for these models by
an error message. This happens when the coefficients of the largest
model reduced to the nested models result in invalid initial estimates
for the nested models (indicated by robustness weights which are all 0).
The comparison between two or more models by \code{\link{anova.lmrob}}
will only be valid if they are fitted to the same dataset.
}
\value{
Basically, an object of class \code{\link{anova}} inheriting from class
\code{\link{data.frame}}.
}
%%\references{ ~put references to the literature/web site here ~ }
\author{Andreas Ruckstuhl}
\seealso{\code{\link{lmrob}}, \code{\link{anova}}.
}
\examples{
data(salinity)
summary(m0.sali <- lmrob(Y ~ . , data = salinity))
anova(m0.sali, Y ~ X1 + X3)
## -> X2 is not needed
(m1.sali <- lmrob(Y ~ X1 + X3, data = salinity))
anova(m0.sali, m1.sali) # the same as before
anova(m0.sali, m1.sali, test = "Deviance")
## whereas 'X3' is highly significant:
m2 <- update(m0.sali, ~ . -X3)
anova(m0.sali, m2)
anova(m0.sali, m2, test = "Deviance")
## Global test [often not interesting]:
anova(m0.sali, update(m0.sali, . ~ 1), test = "Wald")
anova(m0.sali, update(m0.sali, . ~ 1), test = "Deviance")
if(require("MPV")) { ## Montgomery, Peck & Vining datasets
Jet <- table.b13
Jet.rflm1 <- lmrob(y ~ ., data=Jet,
control = lmrob.control(max.it = 500))
summary(Jet.rflm1)
anova(Jet.rflm1, y ~ x1 + x5 + x6, test="Wald")
try( anova(Jet.rflm1, y ~ x1 + x5 + x6, test="Deviance") )
## -> Error in anovaLm.... Please fit the nested models by lmrob
## {{ since all robustness weights become 0 in the nested model ! }}
## Ok: Do as the error message told us:
## test by comparing the two *fitted* models:
Jet.rflm2 <- lmrob(y ~ x1 + x5 + x6, data=Jet,
control=lmrob.control(max.it=100))
anova(Jet.rflm1, Jet.rflm2, test="Deviance")
} # end{"MPV" data}
}
\keyword{robust}
\keyword{models}
\keyword{regression}
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