Akaike weights

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

Weights(x)
Weights(x) <- value

Arguments

x

a numeric vector of any information criterion (such as , , , ) 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 used. The assigned value need not sum to one, but if they are all zero, the result will be invalid (NaN).

Details

‘Akaike weights’, _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:

_i = (_i/2)_r=1^R(_r/2) X w_i = exp(Delta_i / 2) / (sum(exp(Delta_r / 2))

where i is the difference of the i-th model relative to the smallest 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

Kamil Bartoń

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)
#>  model weights 
#> [1] 0.312 0.329 0.044 0.314


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

coef(am)
#>    (Intercept)           dose      I(dose^2)      log(dose) I(log(dose)^2) 
#>   149.56958558    -0.20303260     0.00726326  -219.93533091    32.74938293 

# Assign equal weights to all models:
Weights(am) <- rep(1, 4) # assigned weights are rescaled to sum to 1
Weights(am)
#> unknown model weights 
#> [1] 0.25 0.25 0.25 0.25
coef(am)
#>    (Intercept)           dose      I(dose^2)      log(dose) I(log(dose)^2) 
#>   105.86553402    -0.19150628     0.00726326  -119.12081828    32.74938293 

# Assign dummy weights:
wts <- c(2,1,4,3)
Weights(am) <- wts
coef(am)
#>    (Intercept)           dose      I(dose^2)      log(dose) I(log(dose)^2) 
#>    27.13729609    -0.04582424     0.00726326   -52.21611191    32.74938293 
# Component models are now sorted according to the new weights.
# The same weights assigned again produce incorrect results!
Weights(am) <- wts
coef(am) # wrong!
#>    (Intercept)           dose      I(dose^2)      log(dose) I(log(dose)^2) 
#>   141.62459048    -0.33718833     0.00726326  -186.02552464    32.74938293 
#
Weights(am) <- NULL # reset to original model weights
Weights(am) <- wts 
coef(am) # correct
#>    (Intercept)           dose      I(dose^2)      log(dose) I(log(dose)^2) 
#>    27.13729609    -0.04582424     0.00726326   -52.21611191    32.74938293