VARIABLE SELECTION IN REGRESSION VIA REPEATED DATA SPLITTING

A new algorithm-backward elimination via repeated data splitting (BERD S)-is proposed for variable selection in regression. Initially, the da ta are partitioned into two sets {E, V}, and an exhaustive backward el imination (BE) is performed in E. For each p value cutoff alpha used i n BE, the corresponding fitted model from E is validated in V by compu ting the sum of squared deviations of observed from predicted values. This is repeated m times, and the ct minimizing the sum of the m sums of squares is used as the cutoff in a final BE on the entire data set. BERDS is a modification of the algorithm BECV proposed by Thall, Simo n, and Grier (1992). An extensive simulation study shows that, compare d to BECV, BERDS has a smaller model error and higher probabilities of excluding noise variables, of selecting each of several uncorrelated true predictors, and of selecting exactly one of two or three highly c orrelated true predictors. BERDS is also superior to standard BE with cutoffs .05 or .10, and this superiority increases with the number of noise variables in the data and the degree of correlation among true p redictors. An application is provided for illustration.