Modeling preference heterogeneity using model-based decision trees

This article investigates the usage of a general model-based recursive partitioning algorithm to model preference heterogeneity. We use the algorithm to grow a decision tree based on statistical tests of the stability of individuals’ preference parameters. In particular, we used a Mixed Logit (MIXL) model with alternative-specific attributes at the end leaves of the tree while using individual characteristics as partition variables. This configuration allows us to search for instabilities of the taste parameters across individuals’ characteristics. We conduct a simulation study to investigate the algorithm’s ability to recover different data generating processes with structural breaks in the taste parameters. The results show that the algorithm can correctly recover diverse tree-like data generating processes. Additionally, we applied the algorithm to stated choice data of the preferences for the environmental impact of (hypothetical) energy generation plans in Chile. The results show that the model-based decision tree fits the data better than MIXL in terms of information criteria. Moreover, we show that the derived tree structure depends on the assumptions on the parameters’ distributions. Additionally, we compare the model-based decision tree model with Latent Class (LC) models with and without within-class heterogeneity. Finally, we show that the recursive partitioning algorithm can inform the selection of variables to be included in the LC allocation models.