dredge.Rd
\name{dredge}
\alias{dredge}
\alias{dc}
\alias{V}
\alias{print.model.selection}
\encoding{utf-8}
\newcommand{\Rsq}{\ifelse{latex}{\eqn{R^{2}}{R^2}}{\ifelse{html}{\enc{R²}{R^2}}{R^2}}}
\newcommand{\bq}{\verb{`}\code{#1}\verb{`}}
\title{Automated model selection}
\description{
Generate a model selection table of models with combinations (subsets) of fixed
effect terms in the global model, with optional rules for model inclusion.
}
\usage{
dredge(global.model, beta = c("none", "sd", "partial.sd"), evaluate = TRUE,
rank = "AICc", fixed = NULL, m.lim = NULL, m.min, m.max, subset,
trace = FALSE, varying, extra, ct.args = NULL, ...)
\method{print}{model.selection}(x, abbrev.names = TRUE, warnings = getOption("warn") != -1L, ...)
}
\arguments{
\item{global.model}{a fitted \sQuote{global} model object. See
\sQuote{Details} for a list of supported types. }
\item{beta}{indicates whether and how the coefficients are standardized, and
must be one of \code{"none"}, \code{"sd"} or \code{"partial.sd"}. You can
specify just the initial letter. \code{"none"} corresponds to unstandardized
coefficients, \code{"sd"} and \code{"partial.sd"} to coefficients
standardized by \acronym{SD} and Partial \acronym{SD}, respectively. For
backwards compatibility, logical value is also accepted, \code{TRUE} is
equivalent to \code{"sd"} and \code{FALSE} to \code{"none"}.
See \code{\link{std.coef}}. }
\item{evaluate}{whether to evaluate and rank the models. If \code{FALSE}, a
list of unevaluated \code{call}s is returned. }
\item{rank}{optional custom rank function (returning an information
criterion) to be used instead \code{AICc}, e.g. \code{AIC}, \code{QAIC} or
\code{BIC}.
See \sQuote{Details}. }
\item{fixed}{optional, either a single-sided formula or a character vector
giving names of terms to be included in all models. See \sQuote{Subsetting}. }
\item{m.lim, m.max, m.min}{optionally, the limits \code{c(lower, upper)}
for the number of terms in a single model (excluding the intercept). An
\code{NA} means no limit. See \sQuote{Subsetting}.
Specifying limits as \code{m.min} and \code{m.max} is allowed for backward
compatibility. }
\item{subset}{ logical expression describing models to keep in the resulting
set. See \sQuote{Subsetting}. }
\item{trace}{if \code{TRUE} or \code{1}, all calls to the fitting function
are printed before actual fitting takes place. If \code{trace > 1}, a progress bar
is displayed. }
\item{varying}{ optionally, a named list describing the additional arguments
to vary between the generated models. Item names correspond to the
arguments, and each item provides a list of choices (i.e. \code{list(arg1 =
list(choice1, choice2, ...), ...)}). Complex elements in the choice list
(such as \code{family} objects) should be either named (uniquely) or quoted
(unevaluated, e.g. using \code{\link{alist}}, see \code{\link{quote}}),
otherwise the result may be visually unpleasant. See example in
\code{\link{Beetle}}. }
\item{extra}{ optional additional statistics to include in the result,
provided as functions, function names or a list of such (best if named
or quoted). Similarly as in \code{rank} argument, each function must accept
fitted model object as an argument and return (a value coercible to) a
numeric vector.
These can be e.g. additional information criteria or goodness-of-fit
statistics. The character strings \code{"R^2"} and \code{"adjR^2"} are
treated in a special way, and will add a likelihood-ratio based \Rsq and
modified-\Rsq respectively to the result (this is more efficient than using
\code{\link{r.squaredLR}} directly). }
\item{x}{ a \code{model.selection} object, returned by \code{dredge}. }
\item{abbrev.names}{ should printed term names be abbreviated?
(useful with complex models). }
\item{warnings}{ if \code{TRUE}, errors and warnings issued during the model
fitting are printed below the table (only with \code{pdredge}).
To permanently remove the warnings, set the object's attribute
\code{"warnings"} to \code{NULL}. }
\item{ct.args}{ optional list of arguments to be passed to
\code{\link{coefTable}} (e.g. \code{dispersion} parameter for \code{glm}
affecting standard errors used in subsequent
\code{\link[=model.avg]{model averaging}}).}
\item{\dots}{ optional arguments for the \code{rank} function. Any can be
an unevaluated expression, in which case any \code{x} within it will be
substituted with the current model. }
}
\details{
Models are fitted through repeated evaluation of modified call extracted from
the \code{global.model} (in a similar fashion as with \code{update}). This
approach, while robust in that it can be applied to most model types through the
usual formula interface, may have considerable computational overhead.
Note that the number of combinations grows exponentially with the number of
predictors (\ifelse{latex}{\eqn{2^{N}}}{\ifelse{html}{2ⁿ}{2^N}}, less when
interactions are present, see below).
The fitted model objects are not stored in the result. To get (possibly a subset of)
the models, use \code{\link{get.models}} on the object returned by \code{dredge}.
Another way of getting all the models is to run
\code{lapply(dredge(..., evaluate = FALSE), eval)},
which avoids fitting the models twice.
For a list of model types that can be used as a \code{global.model} see
\link[=MuMIn-models]{the list of supported models}. Modelling functions not storing
\code{call} in their result should be evaluated \emph{via} the wrapper function
created by \code{\link{updateable}}.
\subsection{Information criterion}{
\code{rank} is found by a call to \code{match.fun} and may be specified as a
function or a symbol or a character string specifying
a function to be searched for from the environment of the call to \code{dredge}.
The function \code{rank} must accept a model object as its first argument and
always return a scalar.
}
\subsection{Interactions}{
By default, marginality constraints are respected, so \dQuote{all possible
combinations} include only those containing interactions with their
respective main effects and all lower-order terms.
However, if \code{global.model} makes an exception to this principle (e.g. due
to a nested design such as \code{a / (b + d)}), this will be reflected in the
subset models.
}
\subsection{Subsetting}{
There are three ways to constrain the resulting set of models: setting limits to
the number of terms in a model with \code{m.lim}, binding the
term(s) to all models with \code{fixed}, and more complex rules can be applied
using argument \code{subset}. To be included in the selection table, the model
formulation must satisfy all these conditions.
%%Terms in \code{fixed} argument are applied before the combinations are
%%generated, therefore more efficient than \code{subset}.
\code{subset} can take either a form of an \emph{expression} or a \emph{matrix}.
The latter should be a lower triangular matrix with logical values, where
columns and rows correspond to \code{global.model} terms. Value
\code{subset["a", "b"] == FALSE} will exclude any model containing both terms
\var{a} and \var{b}. \code{demo(dredge.subset)} has examples of using the
\code{subset} matrix in conjunction with correlation matrices to exclude models
containing collinear predictors.
Term names appearing in \code{fixed} and \code{subset} must be given in the
exact form as returned by \code{getAllTerms(global.model)}, which can differ
from the original term names (e.g. the interaction term components are ordered
alphabetically).
In the form of \code{expression}, the argument \code{subset} acts in a similar
fashion to that in the function \code{subset} for \code{data.frames}: model
terms can be referred to by name as variables in the expression, with the
difference being that are interpreted as logical values (i.e. equal to
\code{TRUE} if the term exists in the model).
The expression can contain any of the \code{global.model} term names, as well as
names of the \code{varying} list items. \code{global.model} term names take
precedence when identical to names of \code{varying}, so to avoid ambiguity
\code{varying} variables in \code{subset} expression should be enclosed in
\code{V()} (e.g. \code{V(family) == "Gamma"} assuming that
\code{varying} is something like \code{list(family =} \code{c("Gamma", ...))}).
If item names in \code{varying} are missing, the items themselves are coerced to
names. Call and symbol elements are represented as character values (\emph{via}
\code{deparse}), and everything except numeric, logical, character and
\code{NULL} values is replaced by item numbers (e.g. \code{varying =}
\code{list(family =} \code{list(..., Gamma)} should be referred to as
\code{subset = V(family) == 2}. This can quickly become confusing, therefore it
is recommended to use named lists. \code{demo(dredge.varying)} provides examples.
%% .(+x)
The \code{with(x)} and \code{with(+x)} notation indicates, respectively, any and
all interactions including the main effect term \code{x}. This is only effective
with marginality exceptions. The extended form \code{with(x, order)} allows for
specifying the order of interaction of terms which \code{x} is part of. For
instance, \code{with(b, 2:3)} selects models with at least one second- or
third-order interaction of the variable \code{b}. The second (positional)
argument is coerced to an integer vector. The \dQuote{dot} notation \code{.(x)} is
an alias for \code{with}.
The special variable \ifelse{latex}{\bq{*nvar*}}{\code{`*nvar*`}}
(backtick-quoted), in the \code{subset} expression is equal to the number of
terms in the model (\bold{not} the number of estimated parameters).
To make the inclusion of a model term conditional on the presence of another one,
the function \code{dc} (\dQuote{\bold{d}ependency \bold{c}hain}) can be used in
the \code{subset} expression. \code{dc} takes any number of term names as
arguments, and allows a term to be included only if all preceding ones
are also present (e.g. \code{subset = dc(a, b, c)} allows for models \code{a},
\code{a+b} and \code{a+b+c} but not \code{b}, \code{c}, \code{b+c} or
\code{a+c}).
\code{subset} expression can have a form of an unevaluated \code{call},
\code{expression} object, or a one-sided \code{formula}. See \sQuote{Examples}.
Compound model terms (such as interactions, \sQuote{as-is} expressions within
\code{I()} or smooths in \code{gam}) should be enclosed within curly brackets
(e.g. \code{{s(x,k=2)}}), or \link[=Quotes]{backticks} (like non-syntactic
names, e.g. \ifelse{latex}{
\bq{s(x, k = 2)}
}{
\code{`s(x, k = 2)`}
}), unless they are arguments to \code{.} or \code{dc}.
Backticks-quoted names must match exactly (including whitespace) the term names
as returned by \code{getAllTerms}.
\subsection{\code{subset} expression syntax summary}{
\describe{
\item{\code{a & b}}{ indicates that model terms \var{a} and \var{b} must be
present (see \link[=Logic]{Logical Operators}) }
\item{\code{{log(x,2)}} or \bq{log(x, 2)}}{ represent a complex
model term \code{log(x, 2)}}
\item{\code{V(x)}}{ represents a \code{varying} item \var{x} }
\item{\code{with(x)}}{ indicates that at least one term containing the main
effect term \var{x} must be present }
\item{\code{with(+x)}}{ indicates that all the terms containing the main
effect term \var{x} must be present }
\item{\code{with(x, n:m)}}{ indicates that at least one term containing an
\var{n}-th to \var{m}-th order interaction term of \var{x} must be present }
\item{\code{dc(a, b, c,...)}}{ \sQuote{dependency chain}: \var{b} is allowed only
if \var{a} is present, and \var{c} only if both \var{a} and \var{b} are
present, etc. }
\item{\code{`*nvar*`}}{ the number of terms in the model. }
}
}
To simply keep certain terms in all models, use of argument \code{fixed} is much
more efficient. The \code{fixed} formula is interpreted in the same manner
as model formula and so the terms must not be quoted.
}
\subsection{Missing values}{
Use of \code{na.action = "na.omit"} (\R's default) or \code{"na.exclude"} in
\code{global.model} must be avoided, as it results with sub-models fitted to
different data sets if there are missing values. An error is thrown if it is
detected.
It is a common mistake to give \code{na.action} as an argument in the call
to \code{dredge} (typically resulting in an error from the \code{rank}
function to which the argument is passed through \sQuote{\dots}), while the
correct way
is either to pass \code{na.action} in the call to the global model or to set
it as a \link[=options]{global option}.
}
\subsection{Intercept}{
If present in the \code{global.model}, the intercept will be included in all
sub-models.
}
\subsection{Methods}{
There are \code{\link[=subset.model.selection]{subset}} and
\code{\link[=plot.model.selection]{plot}} methods, the latter creates a
graphical representation of model weights and per-model term sum of weights.
Coefficients can be extracted with \code{coef} or \code{\link{coefTable}}.
}
}
\value{
An object of class \code{c("model.selection", "data.frame")}, being a
\code{data.frame}, where each row represents one model.
See \code{\link{model.selection.object}} for its structure.
}
\author{Kamil Barto\enc{ń}{n}}
\note{
Users should keep in mind the hazards that a \dQuote{thoughtless approach}
of evaluating all possible models poses. Although this procedure is in certain
cases useful and justified, it may result in selecting a spurious \dQuote{best}
model, due to the model selection bias.
\emph{\dQuote{Let the computer find out} is a poor strategy and usually reflects
the fact that the researcher did not bother to think clearly about the problem
of interest and its scientific setting} (Burnham and Anderson, 2002).
}
\seealso{
\code{\link{pdredge}} is a parallelized version of this function (uses a
cluster).
\code{\link{get.models}}, \code{\link{model.avg}}. \code{\link{model.sel}} for
manual model selection tables.
Possible alternatives: \code{\link[glmulti]{glmulti}} in package \pkg{glmulti}
and \code{\link[bestglm]{bestglm}} (\pkg{bestglm}).
\code{\link[leaps]{regsubsets}} in package \pkg{leaps} also performs all-subsets
regression.
\emph{Lasso} variable selection provided by various packages, e.g. \pkg{glmnet},
\pkg{lars} or \pkg{glmmLasso}.
}
\examples{
# Example from Burnham and Anderson (2002), page 100:
# prevent fitting sub-models to different datasets
\dontshow{oop <- }
options(na.action = "na.fail")
fm1 <- lm(y ~ ., data = Cement)
dd <- dredge(fm1)
subset(dd, delta < 4)
# Visualize the model selection table:
\dontshow{ if(require(graphics)) \{ }
par(mar = c(3,5,6,4))
plot(dd, labAsExpr = TRUE)
\dontshow{ \} }
# Model average models with delta AICc < 4
model.avg(dd, subset = delta < 4)
#or as a 95\% confidence set:
model.avg(dd, subset = cumsum(weight) <= .95) # get averaged coefficients
#'Best' model
summary(get.models(dd, 1)[[1]])
\dontrun{
# Examples of using 'subset':
# keep only models containing X3
dredge(fm1, subset = ~ X3) # subset as a formula
dredge(fm1, subset = expression(X3)) # subset as expression object
# the same, but more effective:
dredge(fm1, fixed = "X3")
# exclude models containing both X1 and X2 at the same time
dredge(fm1, subset = !(X1 && X2))
# Fit only models containing either X3 or X4 (but not both);
# include X3 only if X2 is present, and X2 only if X1 is present.
dredge(fm1, subset = dc(X1, X2, X3) && xor(X3, X4))
# the same as above, without "dc"
dredge(fm1, subset = (X1 | !X2) && (X2 | !X3) && xor(X3, X4))
# Include only models with up to 2 terms (and intercept)
dredge(fm1, m.lim = c(0, 2))
}
# Add R^2 and F-statistics, use the 'extra' argument
dredge(fm1, m.lim = c(NA, 1), extra = c("R^2", F = function(x)
summary(x)$fstatistic[[1]]))
# with summary statistics:
dredge(fm1, m.lim = c(NA, 1), extra = list(
"R^2", "*" = function(x) {
s <- summary(x)
c(Rsq = s$r.squared, adjRsq = s$adj.r.squared,
F = s$fstatistic[[1]])
})
)
# Add other information criteria (but rank with AICc):
dredge(fm1, m.lim = c(NA, 1), extra = alist(AIC, BIC, ICOMP, Cp))
\dontshow{options(oop)}
}
\keyword{models}
