Automated model selection
Generate a model selection table of models with combinations (subsets) of fixed effect terms in the global model, with optional rules for model inclusion.
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, ...)
## S3 method for class 'model.selection'
print(x, abbrev.names = TRUE, warnings = getOption("warn") != -1L, ...)global.model |
a fitted ‘global’ model object. See ‘Details’ for a list of supported types. |
beta |
indicates whether and how the coefficients are standardized, and
must be one of |
evaluate |
whether to evaluate and rank the models. If |
rank |
optional custom rank function (returning an information
criterion) to be used instead |
fixed |
optional, either a single-sided formula or a character vector giving names of terms to be included in all models. See ‘Subsetting’. |
m.lim, m.max, m.min |
optionally, the limits |
subset |
logical expression describing models to keep in the resulting set. See ‘Subsetting’. |
trace |
if |
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. |
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 |
x |
a |
abbrev.names |
should printed term names be abbreviated? (useful with complex models). |
warnings |
if |
ct.args |
optional list of arguments to be passed to
|
... |
optional arguments for the |
Models are fitted through repeated evaluation of modified call extracted from
the global.model (in a similar fashion as with 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 (2ⁿ, 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 get.models on the object returned by dredge.
Another way of getting all the models is to run
lapply(dredge(..., evaluate = FALSE), eval),
which avoids fitting the models twice.
For a list of model types that can be used as a global.model see
the list of supported models. Modelling functions not storing
call in their result should be evaluated via the wrapper function
created by updateable.
rank is found by a call to 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 dredge.
The function rank must accept a model object as its first argument and
always return a scalar.
By default, marginality constraints are respected, so “all possible
combinations” include only those containing interactions with their
respective main effects and all lower-order terms.
However, if global.model makes an exception to this principle (e.g. due
to a nested design such as a / (b + d)), this will be reflected in the
subset models.
There are three ways to constrain the resulting set of models: setting limits to
the number of terms in a model with m.lim, binding the
term(s) to all models with fixed, and more complex rules can be applied
using argument subset. To be included in the selection table, the model
formulation must satisfy all these conditions.
subset can take either a form of an expression or a matrix.
The latter should be a lower triangular matrix with logical values, where
columns and rows correspond to global.model terms. Value
subset["a", "b"] == FALSE will exclude any model containing both terms
a and b. demo(dredge.subset) has examples of using the
subset matrix in conjunction with correlation matrices to exclude models
containing collinear predictors.
Term names appearing in fixed and subset must be given in the
exact form as returned by getAllTerms(global.model), which can differ
from the original term names (e.g. the interaction term components are ordered
alphabetically).
In the form of expression, the argument subset acts in a similar
fashion to that in the function subset for 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
TRUE if the term exists in the model).
The expression can contain any of the global.model term names, as well as
names of the varying list items. global.model term names take
precedence when identical to names of varying, so to avoid ambiguity
varying variables in subset expression should be enclosed in
V() (e.g. V(family) == "Gamma" assuming that
varying is something like list(family = c("Gamma", ...))).
If item names in varying are missing, the items themselves are coerced to
names. Call and symbol elements are represented as character values (via
deparse), and everything except numeric, logical, character and
NULL values is replaced by item numbers (e.g. varying =
list(family = list(..., Gamma) should be referred to as
subset = V(family) == 2. This can quickly become confusing, therefore it
is recommended to use named lists. demo(dredge.varying) provides examples.
The with(x) and with(+x) notation indicates, respectively, any and
all interactions including the main effect term x. This is only effective
with marginality exceptions. The extended form with(x, order) allows for
specifying the order of interaction of terms which x is part of. For
instance, with(b, 2:3) selects models with at least one second- or
third-order interaction of the variable b. The second (positional)
argument is coerced to an integer vector. The “dot” notation .(x) is
an alias for with.
The special variable `*nvar*`
(backtick-quoted), in the subset expression is equal to the number of
terms in the model (not the number of estimated parameters).
To make the inclusion of a model term conditional on the presence of another one,
the function dc (“dependency chain”) can be used in
the subset expression. 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. subset = dc(a, b, c) allows for models a,
a+b and a+b+c but not b, c, b+c or
a+c).
subset expression can have a form of an unevaluated call,
expression object, or a one-sided formula. See ‘Examples’.
Compound model terms (such as interactions, ‘as-is’ expressions within
I() or smooths in gam) should be enclosed within curly brackets
(e.g. {s(x,k=2)}), or backticks (like non-syntactic
names, e.g.
`s(x, k = 2)`
), unless they are arguments to . or dc.
Backticks-quoted names must match exactly (including whitespace) the term names
as returned by getAllTerms.
subset expression syntax summarya & bindicates that model terms a and b must be present (see Logical Operators)
{log(x,2)} or `log(x, 2)`
represent a complex
model term log(x, 2)
V(x) represents a varying item x
with(x)indicates that at least one term containing the main effect term x must be present
with(+x)indicates that all the terms containing the main effect term x must be present
with(x, n:m)indicates that at least one term containing an n-th to m-th order interaction term of x must be present
dc(a, b, c,...)‘dependency chain’: b is allowed only if a is present, and c only if both a and b are present, etc.
`*nvar*`the number of terms in the model.
To simply keep certain terms in all models, use of argument fixed is much
more efficient. The fixed formula is interpreted in the same manner
as model formula and so the terms must not be quoted.
Use of na.action = "na.omit" (R's default) or "na.exclude" in
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 na.action as an argument in the call
to dredge (typically resulting in an error from the rank
function to which the argument is passed through ‘...’), while the
correct way
is either to pass na.action in the call to the global model or to set
it as a global option.
If present in the global.model, the intercept will be included in all
sub-models.
An object of class c("model.selection", "data.frame"), being a
data.frame, where each row represents one model.
See model.selection.object for its structure.
Users should keep in mind the hazards that a “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 “best” model, due to the model selection bias.
“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).
Kamil Bartoń
pdredge is a parallelized version of this function (uses a
cluster).
get.models, model.avg. model.sel for
manual model selection tables.
Possible alternatives: glmulti in package glmulti
and bestglm (bestglm).
regsubsets in package leaps also performs all-subsets
regression.
Lasso variable selection provided by various packages, e.g. glmnet, lars or glmmLasso.
# Example from Burnham and Anderson (2002), page 100:
# prevent fitting sub-models to different datasets
options(na.action = "na.fail")
fm1 <- lm(y ~ ., data = Cement)
dd <- dredge(fm1)
subset(dd, delta < 4)
# Visualize the model selection table:
par(mar = c(3,5,6,4))
plot(dd, labAsExpr = TRUE)
# 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]])
## Not run:
# 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))
## End(Not run)
# 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))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.