MMA: Mallow's Model Averaging

Description

Performs model averaging on a set of nested candidate models with the weights vector chosen such that a specific Mallow's criterion is minimized.

Usage

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mma(X, formula=NULL, ycol=1, variance=c("BA","boot"), bsa=200)

Arguments

X

A dataframe or matrix of data.

formula

Formula of the full model.

ycol

Either a character string or integer specifying the column with the outcome variable.

variance

A string specifying whether the variance is estimated due to the formula of Burnham and Anderson ("BA") or based on bootstrapping ("boot").

bsa

A positive integer specifying the number of bootstrap samples used if se="boot".

Details

Mallow's Model Averaging (MMA) considers all nested submodels of the full model as candidate models, i.e if there are 7 variables there are 7 candidate models. The weight vector used to combine the respective estimates is chosen such that a certain Mallow's type criterion is minimized. The final weighted estimate targets to minimize the mean squared prediciton error and is optimal in some sense, see Theorem 1 and Lemma 3 in Hansen, B. (2007, Least Squares Model Averaging, Econometrica, 75:1175-1189).

Note however that the results of MMA depend on the ordering of the regresssors.

Value

Returns an object of class ‘mma’:

coefficients

A matrix of estimated coefficients and standard errors (and bootstrap confidence intervals if se="boot").

averaging.weights

A matrix containing the weights for each models used in the model averaging procedure.

Author(s)

Michael Schomaker

References

Hansen, B. (2007), Least Squares Model Averaging, Econometrica, 75:1175-1189

Examples

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library(lasso2)
data(Prostate)
mma(Prostate,formula=lpsa~.,ycol="lpsa")