getStackingWeights: Get Ensemble Weights via Stacking

In SWS-Methodology/faoswsImputation: Package to perform ensemble imputation for various FAO domains

Description

Weights used to construct the final ensemble from the individual models are computed via stacking.

Usage

getStackingWeights(data, fits, imputationParameters)

Arguments

data	The data object containing the observations to impute.
fits	A list of the fitted values. These may be estimated via leave one out cross-validation or directly.
imputationParameters	A list of the parameters for the imputation algorithms. See defaultImputationParameters() for a starting point.

Details

Traditional stacking proceeds as follows: For each individual byKey (usually country) a set of weights is chosen for the ensemble. The weights are constrained to be positive and to sum to 1, and the final ensemble is constructed by sum(w_i*model_i). The weights should be chosen in a way such that better models are given more importance. Thus, the following criteria is minimized:

sum(errorFunction(|y - w_i*model_i|))

i.e. the errorFunction applied to the difference between the observed values and the ensemble estimate. The errorFunction is typically just x^2, but could be a more complex function.

However, this is roughly equivalent to regression, with a constraint added. In some cases, however, our datasets will be so sparse that we won't be able to perform this optimization (only four observations and 7 valid models, for example, will not have a unique solution). Thus, we instead use a LASSO regression for computing the stacking weights.

Note: if errorType is not "loocv", then stacking will be problematic: much higher weights will be given to flexible models (such as loess or splines) without valid reason.

Value

A data.table containing the weight for each model within each byKey group, as well as a few other (currently unused) statistics.

SWS-Methodology/faoswsImputation documentation built on May 9, 2019, 11:48 a.m.