Hybrid adaptive index model for binary response data

Abstract

We often meet the case in data analysis that the explanatory variables can be occasionally divided into two groups. One group comprises the variables that researchers consider controllable, and the other group comprises those they do not. We call them controllable and uncontrollable variables, respectively. In the study, we deal with binary response data and aim to estimate the relationship between the binary response and controllable variables. Logistic regression model is typically used in binary response data. In addition to that, AIM (Adaptive Index Model; (Tian and Tibshirani Biostatics 12:68–86, 2010)) can also be used in binary response data. Contrast with logistic regression model, AIM can explain the result easier using binary rules but the prediction accuracy of AIM is shown worse than that of logistic regression model. Considering the interpretability and accuracy, it is better to apply AIM to controllable variables and adjust the effect of uncontrollable variables using logistic regression model. Therefore, we propose the method combining AIM and logistic regression model, called hybrid adaptive index model (HAIM), to give best solution.