model.avg: Model averaging

Description

Model averaging based on an information criterion.

Usage

model.avg(object, ..., beta = FALSE, rank = NULL, rank.args = NULL,
    revised.var = TRUE)

Arguments

object

A fitted model object or a list of such objects. Alternatively an object of class model.selection. See Details.

...

more fitted model objects.

beta

Logical, should standardized coefficients be returned?

rank

Optional, custom rank function (information criterion) to use instead of AICc, e.g. BIC or QAIC, may be omitted if object is a model list returned by get.models or a

rank.args

Optional list of arguments for the rank function. If one is an expression, an x within it is substituted with a current model.

revised.var

Logical, indicating whether to use revised formula for standard errors. See par.avg.

Value

An object of class averaging is a list with components:
summarya data.frame with log-likelihood, IC, Delta(IC) and Akaike weights for the component models.
coefficients, se, dfsmatrices of component models' coefficients, their standard errors, and degrees of freedom.
coef.shrinkagea vector of full model-averaged coefficients, see Note.
variable.codesnames of the variables with numerical codes used in summary.
avg.modelthe model averaged parameters. A data.frame containing averaged coefficients, unconditional standard error, adjusted SE (if dfs are available) and z-values (coefficient and SE) and significance (assuming a normal error distribution).
importancerelative importance of the predictor variables, calculated as a sum of the Akaike weights over all of the models in which the parameter of interest appears.
term.namescharacter vector giving names of all terms in the model.
x, formulathe model matrix and formula corresponding to the one that would be used in a single model. formula contains only the averaged coefficients.
residualsmodel averaged residuals (response minus fitted values).
callthe matched call.
In addition, the object has following attributes:
mLista list of component model objects.
betalogical, were standardized coefficients used?
revised.varif TRUE, the standard errors were calculated with the revised formula (See par.avg).

encoding

utf-8

Details

model.avg has been tested to work with the fitted objects from the following modelling functions: lm, glm; 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); and several models within the class unmarkedFit (unmarked). Other classes are also likely to be supported, in particular those inheriting from one of the above classes. See the vignette Extending MuMIn's functionality for a demonstration on how to provide support for other types of models.

model.avg may be used with a list of models, but also directly with a model.selection object returned by dredge. In the latter case, the models from the model selection table are evaluated (with a call to get.models) prior to averaging. A warning is given if the subset argument is not provided, and the default delta <= 4<="" code=""> will be used.

rank is found by a call to match.fun and typically is 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 lapply. rank must be a function able to accept model as a first argument and must always return a scalar.

Several standard methods for fitted model objects exist for class averaging, including summary, predict, coef, confint, formula, residuals, vcov. The coef method a accepts argument full, if set to TRUE the full model-averaged coefficients are returned, rather than subset-averaged ones. logLik returns a list of logLik objects for the component models.

References

Burnham, K. P. and Anderson, D. R (2002) Model selection and multimodel inference: a practical information-theoretic approach. 2nd ed. New York, Springer-Verlag.

Examples

Run this code

# Example from Burnham and Anderson (2002), page 100:
data(Cement)
fm1 <- lm(y ~ ., data = Cement)
(ms1 <- dredge(fm1))

#models with delta.aicc < 4
summary(model.avg(get.models(ms1, subset = delta < 4))) # get averaged coefficients

#or as a 95\% confidence set:
confset.95p <- get.models(ms1, cumsum(weight) <= .95)

avgmod.95p <- model.avg(confset.95p) # get averaged coefficients
confint(avgmod.95p)


# The same result
model.avg(ms1, cumsum(weight) <= .95)

# using BIC (Schwarz's Bayesian criterion) to rank the models
BIC <- function(x) AIC(x, k=log(length(residuals(x))))
model.avg(confset.95p, rank=BIC)
# the same result, using AIC directly, with argument k
# 'x' in a quoted 'rank' argument is substituted with a model object
# (in this case it does not make much sense as the number of observations is
# common to all models)
model.avg(confset.95p, rank=AIC, rank.args=alist(k=log(length(residuals(x)))))

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