Efficient Variable Selection Method for Exposure Variables on Binary Data

Abstract

In this paper, we propose a new variable selection method for "robust" exposure variables. We define "robust" as property that the same variable can select among original data and perturbed data. There are few studies of effective for the selection method. The problem that selects exposure variables is almost the same as a problem that extracts correlation rules without robustness. [Brin 97] is suggested that correlation rules are possible to extract efficiently using chi-squared statistic of contingency table having monotone property on binary data. But the chi-squared value does not have monotone property, so it's is easy to judge the method to be not independent with an increase in the dimension though the variable set is completely independent, and the method is not usable in variable selection for robust exposure variables. We assume anti-monotone property for independent variables to select robust independent variables and use the apriori algorithm for it. The apriori algorithm is one of the algorithms which find association rules from the market basket data. The algorithm use anti-monotone property on the support which is defined by association rules. But independent property does not completely have anti-monotone property on the AIC of independent probability model, but the tendency to have anti-monotone property is strong. Therefore, selected variables with anti-monotone property on the AIC have robustness. Our method judges whether a certain variable is exposure variable for the independent variable using previous comparison of the AIC. Our numerical experiments show that our method can select robust exposure variables efficiently and precisely.