Computes model weights based on a cross-validation-like procedure.
stackingWeights(object, ..., data, R, p = 0.5)
two or more fitted
a data frame containing the variables in the model, used for fitting and prediction.
the number of replicates.
the proportion of the
Each model in a set is fitted to the training data: a subset of
p * N
data. From these models a prediction is produced on
the remaining part of
data (the test
or hold-out data). These hold-out predictions are fitted to the hold-out
observations, by optimising the weights by which the models are combined. This
process is repeated
R times, yielding a distribution of weights for each
model (which Smyth & Wolpert (1998) referred to as an ‘empirical Bayesian
estimate of posterior model probability’). A mean or median of model weights for
each model is taken and re-scaled to sum to one.
A matrix with two rows, containing model weights
This approach requires a sample size of at least 2x the number of models.
Carsten Dormann, Kamil Bartoń
Wolpert, D. H. (1992) Stacked generalization. Neural Networks, 5: 241-259.
Smyth, P. & Wolpert, D. (1998) An Evaluation of Linearly Combining Density Estimators via Stacking. Technical Report No. 98-25. Information and Computer Science Department, University of California, Irvine, CA.
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.
Other model weights:
#simulated Cement dataset to increase sample size for the training data fm0 <- glm(y ~ X1 + X2 + X3 + X4, data = Cement, na.action = na.fail) dat <- as.data.frame(apply(Cement[, -1], 2, sample, 50, replace = TRUE)) dat$y <- rnorm(nrow(dat), predict(fm0), sigma(fm0)) # global model fitted to training data: fm <- glm(y ~ X1 + X2 + X3 + X4, data = dat, na.action = na.fail) # generate a list of *some* subsets of the global model models <- lapply(dredge(fm, evaluate = FALSE, fixed = "X1", m.lim = c(1, 3)), eval) wts <- stackingWeights(models, data = dat, R = 10) ma <- model.avg(models) Weights(ma) <- wts["mean", ] predict(ma)
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