BGweights: Bates-Granger minimal variance model weights

BGWeightsR Documentation

Bates-Granger minimal variance model weights


Computes empirical weights based on out of sample forecast variances, following Bates and Granger (1969).


BGWeights(object, ..., data, force.update = FALSE)


object, ...

two or more fitted glm objects, or a list of such, or an "averaging" object.


a data frame containing the variables in the model.


if TRUE, the much less efficient method of updating glm function will be used rather than directly via This only applies to glms, in case of other model types update is always used.


Bates-Granger model weights are calculated using prediction covariance. To get the estimate of prediction covariance, the models are fitted to randomly selected half of data and prediction is done on the remaining half. These predictions are then used to compute the variance-covariance between models, \Sigma. Model weights are then calculated as w_BG = (1' \Sigma{^-1} 1){^-1} 1 \Sigma{^-1} , where 1 a vector of 1-s.

Bates-Granger model weights may be outside of the [0,1] range, which may cause the averaged variances to be negative. Apparently this method works best when data is large.


A numeric vector of model weights.


For matrix inversion, MASS::ginv() is more stable near singularities than solve. It will be used as a fallback if solve fails and MASS is available.


Carsten Dormann, Kamil Bartoń


Bates, J. M. and Granger, C. W. J. 1969 The combination of forecasts. Journal of the Operational Research Society 20, 451-468.

Dormann, C. et al. (2018) Model averaging in ecology: a review of Bayesian, information-theoretic, and tactical approaches for predictive inference. Ecological Monographs 88, 485–504.

See Also

Weights, model.avg

Other model weights: bootWeights(), cos2Weights(), jackknifeWeights(), stackingWeights()


fm <- glm(Prop ~ mortality + dose, family = binomial, Beetle, na.action =
models <- lapply(dredge(fm, evaluate = FALSE), eval)
ma <- model.avg(models)

# this produces warnings because of negative variances:
Weights(ma) <- BGWeights(ma, data = Beetle)
coefTable(ma, full = TRUE)

# SE for prediction is not reliable if some or none of coefficient's SE
# are available
predict(ma, data =, = TRUE)
coefTable(ma, full = TRUE)

MuMIn documentation built on March 31, 2023, 8:33 p.m.