MuMIn (version 1.48.11)

Weights: Akaike weights

Description

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

Usage

Weights(x)
Weights(x) <- value

Value

For the extractor, a numeric vector of normalized likelihoods.

Arguments

x

a numeric vector of any information criterion (such as AIC, AIC\(_{c}\), 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).

Author

Kamil Bartoń

Details

‘Akaike weights’, \(\omega_{i}\), 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:

$$ \omega_i = \frac{\exp(\Delta_i/2)}{\sum_{r=1}^{R}\exp(\Delta_r/2)} $$

where \(\Delta_{i}\) 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.

See Also

sw, weighted.mean

armWeights, bootWeights, BGWeights, cos2Weights, jackknifeWeights and stackingWeights can be used to produce various kinds of model weights.

Not to be confused with weights, 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