Tree-Structured Model with Unbiased Variable Selection and Interaction Detection for Ranking Data

In this article, we propose a tree-structured method for either complete or partial rank data that incorporates covariate information into the analysis. We use conditional independence tests based on hierarchical log-linear models for three-way contingency tables to select split variables and cut points, and apply a simple Bonferroni rule to declare whether a node worths splitting or not. Through simulations, we also demonstrate that the proposed method is unbiased and effective in selecting informative split variables. Our proposed method can be applied across various fields to provide a flexible and robust framework for analyzing rank data and understanding how various factors affect individual judgments on ranking. This can help improve the quality of products or services and assist with informed decision making.