model.avg: Model averaging

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

Model averaging based on an information criterion.

Usage

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model.avg(object, ..., revised.var = TRUE)

## Default S3 method:
model.avg(object, ..., beta = c("none", "sd", "partial.sd"),
    rank = NULL, rank.args = NULL, revised.var = TRUE,
    dispersion = NULL, ct.args = NULL)

## S3 method for class 'model.selection'
model.avg(object, subset, fit = FALSE, ..., revised.var = TRUE)

Arguments

object

a fitted model object or a list of such objects, or a "model.selection" object. See ‘Details’.

...

for default method, more fitted model objects. Otherwise, arguments that are passed to the default method.

beta

indicates whether and how the component models' coefficients should be standardized. See the argument's description in dredge.

rank

optionally, a rank function (returning an 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 "model.selection" object. See ‘Details’.

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.

dispersion

the dispersion parameter for the family used. See summary.glm. This is used currently only with glm, is silently ignored otherwise.

ct.args

optional list of arguments to be passed to coefTable (besides dispersion).

subset

see subset method for "model.selection" object.

fit

if TRUE, the component models are fitted using get.models. See ‘Details’.

Details

model.avg may be used either with a list of models, or directly with a model.selection object (e.g. returned by dredge). In the latter case, the models from the model selection table are not evaluated unless the argument fit is set to TRUE or some additional arguments are present (such as rank or dispersion). This results in much faster calculation, but has certain drawbacks, because the fitted component model objects are not stored, and some methods (e.g. predict, fitted, model.matrix or vcov) would not be available with the returned object. Otherwise, get.models is called prior to averaging, and ... are passed to it.

For a list of model types that are accepted see list of supported models.

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

Several standard methods for fitted model objects exist for class averaging, including summary, predict, coef, confint, formula, and vcov.

coef, vcov, confint and coefTable accept argument full that if set to TRUE, the full model-averaged coefficients are returned, rather than subset-averaged ones (when full = FALSE, being the default).

logLik returns a list of logLik objects for the component models.

Value

An object of class "averaging" is a list with components:

msTable

a data.frame with log-likelihood, IC, Δ_IC and ‘Akaike weights’ for the component models. Its attribute "term.codes" is a named vector with numerical representation of the terms in the row names of msTable.

coefficients

a matrix of model-averaged coefficients. “full” coefficients in first row, “subset” coefficients in second row. See ‘Note’

coefArray

a 3-dimensional array of component models' coefficients, their standard errors and degrees of freedom.

importance

object of class importance containing relative importance values of each term (including interactions), calculated as a sum of the Akaike weights over all of the models in which the term appears.

formula

a formula corresponding to the one that would be used in a single model. The formula contains only the averaged (fixed) coefficients.

call

the matched call.

The object has following attributes:

rank

the rank function used.

modelList

optionally, a list of all component model objects. Only if the object was created with model objects (and not model selection table).

beta

Corresponds to the function argument.

nobs

number of observations.

revised.var

Corresponds to the function argument.

Note

The ‘subset’ (or ‘conditional’) average only averages over the models where the parameter appears. An alternative, the ‘full’ average assumes that a variable is included in every model, but in some models the corresponding coefficient (and its respective variance) is set to zero. Unlike the ‘subset average’, it does not have a tendency of biasing the value away from zero. The ‘full’ average is a type of shrinkage estimator and for variables with a weak relationship to the response they are smaller than ‘subset’ estimators.

Averaging models with different contrasts for the same factor would yield nonsense results, currently no checking for contrast consistency is done.

print method provides a concise output (similarly as for lm). To print more details use summary function, and confint to get confidence intervals.

Author(s)

Kamil Bartoń

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.

Lukacs, P. M., Burnham K. P. and Anderson, D. R. (2009) Model selection bias and Freedman’s paradox. Annals of the Institute of Statistical Mathematics 62(1): 117–125.

See Also

See par.avg for more details of model averaged parameter calculation.

dredge, get.models
AICc has examples of averaging models fitted by REML.

modavg in package AICcmodavg, and coef.glmulti in package glmulti also perform model averaging.

Examples

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

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

#or as a 95% confidence set:
avgmod.95p <- model.avg(ms1, cumsum(weight) <= .95)
confint(avgmod.95p)

## Not run: 
# The same result, but re-fitting the models via 'get.models'
confset.95p <- get.models(ms1, cumsum(weight) <= .95)
model.avg(confset.95p)

# Force re-fitting the component models
model.avg(ms1, cumsum(weight) <= .95, fit = TRUE)
# Models are also fitted if additional arguments are given
model.avg(ms1, cumsum(weight) <= .95, rank = "AIC")

## End(Not run)

## Not run: 
# 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)))))

## End(Not run)

MuMIn documentation built on Jan. 31, 2018, 1:03 a.m.