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The nonnegative garrote (NNG) is among the first approaches that combinevariable selection and shrinkage of regression estimates. When more than thederivation of a predictor is of interest, NNG has some conceptual advantagesover the popular lasso. Nevertheless, NNG has received little attention. Theoriginal NNG relies on least-squares (OLS) estimates, which are highly variablein data with a high degree of multicollinearity (HDM) and do not exist inhigh-dimensional data (HDD). This might be the reason that NNG is not used insuch data. Alternative initial estimates have been proposed but hardly used inpractice. Analyzing three structurally different data sets, we demonstratedthat NNG can also be applied in HDM and HDD and compared its performance withthe lasso, adaptive lasso, relaxed lasso, and best subset selection in terms ofvariables selected, regression estimates, and prediction. Replacing OLS byridge initial estimates in HDM and lasso initial estimates in HDD helped NNGselect simpler models than competing approaches without much increase inprediction errors. Simpler models are easier to interpret, an important issuefor descriptive modelling. Based on the limited experience from three datasets,we assume that the NNG can be a suitable alternative to the lasso and itsextensions. Neutral comparison simulation studies are needed to betterunderstand the properties of variable selection methods, compare them andderive guidance for practice.

Exhuming nonnegative garrote from oblivion using suitable initial estimates- illustration in low and high-dimensional real data