Given the standard linear model the traditional way of deciding whether to include the jth covariate is to apply the Ftest to decide whether the corresponding beta coefficient is zero. The Gaussian covariate method is completely different. The question as to whether the beta coefficient is or is not zero is replaced by the question as to whether the covariate is better or worse than i.i.d. Gaussian noise. The Pvalue for the covariate is the probability that Gaussian noise is better. Surprisingly this can be given exactly and it is the same a the Pvalue for the classical model based on the Fdistribution. The Gaussian covariate Pvalue is model free, it is the same for any data set. Using the idea it is possible to do covariate selection for a small number of covariates 25 by considering all subsets. Post selection inference causes no problems as the Pvalues hold whatever the data. The idea extends to stepwise regression again with exact probabilities. In the simplest version the only parameter is a specified cutoff Pvalue which can be interpreted as the probability of a false positive being included in the final selection. For more information see the web site below and the accompanying papers: L. Davies and L. Duembgen, "Covariate Selection Based on a Modelfree Approach to Linear Regression with Exact Probabilities", 2022, <arxiv:2202.01553>. L. Davies, "Linear Regression, Covariate Selection and the Failure of Modelling", 2022, <arXiv:2112.08738>.
Package details 


Author  Laurie Davies [aut, cre] 
Maintainer  Laurie Davies <laurie.davies@unidue.de> 
License  GPL3 
Version  0.1.7 
Package repository  View on CRAN 
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