MuMIn (version 1.6.1)

dredge: Automated model selection

Description

Generate a set of models with combinations of the terms in the global model, with optional rules for inclusion.

Usage

dredge(global.model, beta = FALSE, evaluate = TRUE, rank = "AICc",
    fixed = NULL, m.max = NA, m.min = 0, subset, marg.ex = NULL,
    trace = FALSE, varying, extra, ...)

## S3 method for class 'model.selection':
print(x, abbrev.names = TRUE, ...)

Arguments

global.model

a fitted global model object. See Details for a list of supported types.

beta

logical, should standardized coefficients be returned?

evaluate

whether to evaluate and rank the models. If FALSE, a list of model calls is returned.

rank

optional custom rank function (information criterion) to be used instead AICc, e.g. QAIC or BIC. See Details.

fixed

optional, either a single sided formula or a character vector giving names of terms to be included in all models.

m.max, m.min

optionally the maximum and minimum number of terms in a single model (excluding the intercept), m.max defaults to the number of terms in global.model.

subset

logical expression describing models to keep in the resulting set. See Details.

marg.ex

a character vector specifying names of variables for which NOT to check for marginality restrictions when generating model formulas. If this argument is set to TRUE, all combinations of terms are used (i.e. no checking).

trace

if TRUE, all calls to the fitting function (i.e. updated global.model calls) are printed before actual fitting takes place.

varying

optionally, a named list describing the additional arguments to vary between the generated models. Names are the names of the arguments, and each item provides a list of choices. Complex items in the choice list (such as family objects) sh

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 rank argument, each function must accept fitted object model as an argument and ret

x

a model.selection object, returned by dredge.

abbrev.names

should variable names be abbreviated when printing? (useful with many variables).

...

optional arguments for the rank function. Any can be an expression (of mode call), in which case any x within it will be substituted with a current model.

Value

• dredge returns an object of class model.selection, being a data.frame with models' coefficients (or presence/NA for factors), df - number of parameters, log-likelihood, the information criterion value, delta-IC and Akaike weight. Models are ordered by the value of the information criterion specified by rank (lowest on top).

  The attribute "calls" is a list containing the model calls used (arranged in the same order as the models). Other attributes: "global" - the global.model object, "rank" - the rank function used, and "call" - the matched call.

encoding

utf-8

Details

Fitted model objects that can be used as a global.model include those returned by lm, glm (package stats); gam, gamm (mgcv); gamm4 (gamm4); lme, gls (nlme); lmer (lme4); rlm, glm.nb, polr (MASS); multinom (nnet); sarlm, spautolm (spdep); glmmML (glmmML); coxph, survreg (survival); rq (quantreg); and most models from package unmarked. gamm and gamm4 should be evaluated via the wrapper MuMIn::gamm.

Models are fitted one by one through repeated evaluation of modified calls to the global.model (in a similar fashion as with update). This method, while robust in that it can be applied to a variety of different model object types is not very efficient, and may be time-intensive.

Note that the number of combinations grows exponentially with number of predictor variables (latex{$2^{N}$}{2^N}). Because there can be potentially a large number of models to evaluate, to avoid memory overflow the fitted model objects are not stored in the result. To get (a subset of) the models, use get.models on the object returned by dredge.

Handling interactions, dredge respects marginality constraints, so all possible combinations do not include models containing interactions without their respective main effects. This behaviour can be altered by marg.ex argument. It can be used to allow for simple nested designs. For example, with global model of form a / (x + z), use marg.ex = "a" and fixed = "a".

rank is found by a call to match.fun and may be specified as a function or a symbol (e.g. a back-quoted name) or a character string specifying a function to be searched for from the environment of the call to dredge. Function rank must be able to accept model as a first argument and must always return a scalar. Typical choice for rank would be "AIC", "QAIC" or "BIC" (stats or nlme).

The argument subset acts in a similar fashion to that in the function subset for data.frames: the model terms can be referred to by name as variables in the expression, with the difference that they are always logical (i.e. TRUE if a term exists in the model). The expression can contain any of the global.model terms (use getAllTerms(global.model) to list them). It can have a form of an unevaluated call, expression object, or a one sided formula. See Examples. Compound model terms (such as as-is expressions within I() or the smooths in gam) should be treated as non-syntactic names and enclosed in back-ticks (see Quotes). Mind the spacing, names must match exactly the term names in model's formula. To simply keep certain variables in all models, use of fixed is preferred.

Use of na.action = na.omit (R's default) in global.model should be avoided, as it results with sub-models fitted to different data sets, if there are missing values. In versions >= 0.13.17 a warning is given in such a case.

See Also

get.models, model.avg.

There are subset and plot methods.

Possible alternatives: glmulti in package glmulti and bestglm (bestglm), or aictab (AICcmodavg) and ICtab (bbmle) for "hand-picked" model selection tables.

regsubsets in package leaps also performs all-subsets regression.

Examples

# Example from Burnham and Anderson (2002), page 100:
data(Cement)
fm1 <- lm(y ~ ., data = Cement)
dd <- dredge(fm1)
subset(dd, delta < 4)

# Visualize the model selection table:
if(require(graphics))
plot(dd)


# Model average models with delta AICc < 4
model.avg(get.models(dd, subset = delta < 4))

#or as a 95\% confidence set:
confset.95p <- get.models(dd, cumsum(weight) <= .95)

model.avg(confset.95p) # get averaged coefficients

#'Best' model
summary(confset.95p[[1]])

# Examples of using 'subset':
# exclude models containing both X1 and X2
dredge(fm1, subset = !(X1 & X2))
# 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")

#Reduce the number of generated models, by including only those with
# up to 2 terms (and intercept)
dredge(fm1, m.max = 2)


# Add R^2 and F-statistics, use the 'extra' argument
dredge(fm1, m.max = 1, extra = c("R^2", F = function(x) summary(x)$fstatistic[[1]]))

# with summary statistics:
dredge(fm1, m.max = 1, extra = list(
    "R^2", "*" = function(x) {
        s <- summary(x)
        c(Rsq = s$r.squared, adjRsq = s$adj.r.squared, F = s$fstatistic[[1]])
    })
)


# with other information criterions:

# there is no BIC in R < 2.13.0, so need to add it:
if(!exists("BIC", mode="function"))
    BIC <- function(object, ...) AIC(object, k = log(length(resid(object))))

dredge(fm1, m.max = 1, extra = alist(AIC, BIC, ICOMP, Cp))