  In this paper, we propose a hybrid bankcard response model, which integrates
decision tree based chi-square automatic interaction detection (CHAID) into
logistic regression. In the first stage of the hybrid model, CHAID analysis is
used to detect the possibly potential variable interactions. Then in the second
stage, these potential interactions are served as the additional input
variables in logistic regression. The motivation of the proposed hybrid model
is that adding variable interactions may improve the performance of logistic
regression. To demonstrate the effectiveness of the proposed hybrid model, it
is evaluated on a real credit customer response data set. As the results
reveal, by identifying potential interactions among independent variables, the
proposed hybrid approach outperforms the logistic regression without searching
for interactions in terms of classification accuracy, the area under the
receiver operating characteristic curve (ROC), and Kolmogorov-Smirnov (KS)
statistics. Furthermore, CHAID analysis for interaction detection is much more
computationally efficient than the stepwise search mentioned above and some
identified interactions are shown to have statistically significant predictive
power on the target variable. Last but not least, the customer profile created
based on the CHAID tree provides a reasonable interpretation of the
interactions, which is the required by regulations of the credit industry.
Hence, this study provides an alternative for handling bankcard classification
tasks.
