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Variable Selection with Log-Density in Logistic Regression Model

We present methods to study the log-density ratio of the conditional densities of the predictors given the response variable in the logistic regression model. This allows us to select which predictors are needed and how they should be included in the model. If the conditional distributions are skewed, the distributions can be considered as gamma distributions. A simulation study shows that the linear and log terms are required in general. If the conditional distributions of x j y for the two groups overlap signiﬁcantly, we need both the linear and log terms; however, only the linear or log term is needed in the model if they are well separated.