Regression Tree Model for Analysis of Demand with Heterogeneity and Censorship

Abstract

In this research we analyze new approach for prediction of demand. In the studied market of performing arts the observed demand is limited by capacity of the house. Then one needs to account for demand censorship to obtain unbiased estimates of demand function parameters. The presence of consumer segments with different purposes of going to the theatre and willingness-to-pay for performance and ticket characteristics causes a heterogeneity in theatre demand. We propose an estimator for prediction of demand that accounts for both demand censorship and preferences heterogeneity. The estimator is based on the idea of classification and regression trees and bagging prediction aggregation extended for prediction of censored data. Our algorithm predicts and combines predictions for both discrete and continuous parts of censored data. We show that our estimator performs better in terms of prediction accuracy compared with estimators which accounts either for censorship, or heterogeneity only. The proposed approach is helpful for finding product segments and optimal price setting.