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Model selection consistency, i.e. selecting truly relevant variables is important for a correct interpretation and further downstream analysis, e.g. performing a subsequent pathway analysis.
However, despite parameter estimation consistency, model selection consistency, i.e. selecting the variables that truly contribute to a PC, also plays an important role.
However, even though the lasso does not fulfill the oracle property and can not achieve model selection consistency in high-dimensional data, it selects the truly relevant variables with high probability (Benner et al., 2010).
This paper deals with the model selection consistency of Nonnegative Elastic Net (proposed by imposing nonnegative constraint to the regression parameters) in general setting where p (the number of predictors), q (the number of predictors with non-zero coefficients in the true linear model) and n (sample size) all go to infinity.
The lasso is a popular method whose model selection consistency has been widely explored in the literature (Meinshausen and Bühlmann, 2006; Zhao and Yu, 2006).
Meinshausen and Bühlmann (2010) showed that this additional randomization achieves model selection consistency even in situations where the necessary conditions for consistency of the lasso are violated.
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In a typical setting of linear regression, it has been shown that such an excessive l1-penalty can affect the consistency of model selection [ 15- 18].
Model selection and model averaging are used to investigate data consistency, to identify a reference value of the Planck constant, and to include the model uncertainty in the error budget.
35 The quasi-information criterion 'QIC u' was one criterion for model selection, 32 aiming for the lowest value along with parsimony and consistency with the prior literature.
Prior to model selection, we first conducted GLMs with each of the following environmental factors serving as response variables to determine the consistency of ecological differences between fragmentation regimes: piscivore density, Gambusia density, salinity, turbidity, pH, and dissolved oxygen.
Model selection criterion.
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