A variable selection proposal for multiple linear regression analysis

Steel S.J. ; Uys D.W. (2011)


Variable selection in multiple linear regression models is considered. It is shown that for the special case of orthogonal predictor variables, an adaptive pre-test-type procedure proposed by Venter and Steel [Simultaneous selection and estimation for the some zeros family of normal models, J. Statist. Comput. Simul. 45 (1993), pp. 129-146] is almost equivalent to least angle regression, proposed by Efron et al. [Least angle regression, Ann. Stat. 32 (2004), pp. 407-499]. A new adaptive pre-test-type procedure is proposed, which extends the procedure of Venter and Steel to the general non-orthogonal case in a multiple linear regression analysis. This new procedure is based on a likelihood ratio test where the critical value is determined data-dependently. A practical illustration and results from a simulation study are presented. © 2011 Copyright Taylor and Francis Group, LLC.

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