Weights: Akaike weights

In MuMIn: Multi-Model Inference

Akaike weights

Description

Calculate, extract or set normalized model likelihoods (‘Akaike weights’).

Usage

Weights(x)
Weights(x) <- value

Arguments

x	a numeric vector of any information criterion (such as \AIC, \AICc, \QAIC, \BIC) values, or objects returned by functions like AIC. There are also methods for extracting ‘Akaike weights’ from "model.selection" or "averaging" objects.
value	numeric, the new weights for the "averaging" object or NULL to reset the weights based on the original \IC used. The assigned value need not sum to one, but if they are all zero, the result will be invalid (NaN).

Details

‘Akaike weights’, \myequation\omega_iXw_i, of a model i can be interpreted as the probability that the model is the best (approximating) model given the data and the set of all models considered. The weights are calculated as:

\mydequation \omega

_i = \frac\exp(\Delta_i/2)\sum_r=1^R\exp(\Delta_r/2) X w_i = exp(Delta_i / 2) / (sum(exp(Delta_r / 2))

where \DeltaICi is the \IC difference of the i-th model relative to the smallest \IC value in the set of R models.

The replacement version of Weights can assign new weights to an "averaging" object, affecting coefficient values and the order of component models. Upon assignment, the weights are normalised to sum to one.

Value

For the extractor, a numeric vector of normalized likelihoods.

Note

Assigning new weights changes the model order accordingly, so reassigning weights to the same object must take this new order into account, otherwise the averaged coefficients will be calculated incorrectly. To avoid this, either re-set the model weights by assigning NULL, or sort the new weights using the (decreasing) order of the previously assigned weights.

Author(s)

Kamil Bartoń

See Also

\lcode

sw, \lcodeweighted.mean

\lcode

armWeights, \lcodebootWeights, \lcodeBGWeights, \lcodecos2Weights, \lcodejackknifeWeights and \lcodestackingWeights can be used to produce various kinds of model weights.

Not to be confused with \lcodeweights, which extracts fitting weights from model objects.

Examples

fm1 <- glm(Prop ~ dose, data = Beetle, family = binomial)
fm2 <- update(fm1, . ~ . + I(dose^2))
fm3 <- update(fm1, . ~ log(dose))
fm4 <- update(fm3, . ~ . + I(log(dose)^2))

round(Weights(AICc(fm1, fm2, fm3, fm4)), 3)


am <- model.avg(fm1, fm2, fm3, fm4, rank = AICc)

coef(am)

# Assign equal weights to all models:
Weights(am) <- rep(1, 4) # assigned weights are rescaled to sum to 1
Weights(am)
coef(am)

# Assign dummy weights:
wts <- c(2,1,4,3)
Weights(am) <- wts
coef(am)
# Component models are now sorted according to the new weights.
# The same weights assigned again produce incorrect results!
Weights(am) <- wts
coef(am) # wrong!
#
Weights(am) <- NULL # reset to original model weights
Weights(am) <- wts 
coef(am) # correct

MuMIn documentation built on April 1, 2025, 3 a.m.