Penalized generalized least squares for model selection under restricted randomizationPenalized generalized least squares for model selection under restricted randomization
Faculty of Applied Economics
Preprint / Isaac Newton Institute for Mathematical Sciences ; NI 11032
University of Antwerp
For model selection purposes in experimental contexts, researchers often use step- wise regression or subset selection. With currently available software, this has to be done manually and often involves numerous model estimations in situations involv- ing restricted randomization, such as block experiments and split-plot experiments. Moreover, these selection procedures ignore the stochastic errors inherited in the variable selection stage. This leads to incorrect standard errors. In this paper, we investigate the usefulness of penalized least squares estimation, which performs model selection and model estimation simultaneously. Therefore, the method results in correct standard errors. A key property of the penalized least squares estimation approach is that it possesses the so-called oracle property, which means that it works as well as if the correct sub-model were known. We study the performance of the approach using various practical examples, and investigate its properties in a simu- lation study.