Joint learning from heterogeneous rank data: The sparse fused rank-ordered logit model

The rank-ordered logit (ROL) model is frequently used to aggregate rankings from multiple individuals into a single ranking that corresponds to the unobserved utility derived from the ranked alternatives. When these individuals exhibit heterogeneous preferences, they can be grouped to reduce bias. However, the common practice of fitting ROL models separately for each group may overlook shared patterns across groups, resulting in a loss of information. We introduce the sparse fused rank-ordered logit (SFROL) model, an extension of the ROL model, that allows joint learning from heterogeneous ranking data, where information from different groups is utilised to achieve better model performance. In this framework, the observed rankings are modelled as a function of covariates pertaining to the ranked alternatives. By imposing penalties on the likelihood function, we allow for both the sharing of information on the corresponding coefficients across groups and the shrinkage of the coefficients to zero to improve model interpretability, parameter estimation and prediction. Simulation studies generally indicate superior performance of the proposed method compared to existing approaches across a wide variety of scenarios. The use and interpretation of the method are illustrated on a sweet potato consumer preference application. An R package containing the proposed methodology can be found at https://CRAN.R-project.org/package=SFPL .