  Screening experiments are useful for screening out a small number of truly
important factors from a large number of potentially important factors. The
Gauss-Dantzig Selector (GDS) is often the preferred analysis method for
screening experiments. Just considering main-effects models can result in
erroneous conclusions, but including interaction terms, even if restricted to
two-factor interactions, increases the number of model terms dramatically and
challenges the GDS analysis. We propose a new analysis method, called
Gauss-Dantzig Selector Aggregation over Random Models (GDS-ARM), which performs
a GDS analysis on multiple models that include only some randomly selected
interactions. Results from these different analyses are then aggregated to
identify the important factors. We discuss the proposed method, suggest choices
for the tuning parameters, and study its performance on real and simulated
data.
