Integrating covariate effects in mixtures of Mallows model with Spearman for the analysis of preference rankings
Conference
65th ISI World Statistics Congress 2025
Format: IPS Abstract - WSC 2025
Keywords: mixtures, rankings
Session: IPS 982 - PREFSTAT: Advanced Statistical Learning for Preference Rankings
Monday 6 October 10:50 a.m. - 12:30 p.m. (Europe/Amsterdam)
Abstract
We introduce an extension of the Mixtures of Mallows model with Spearman distance (MMS) that incorporates respondents' covariates into the analysis of ranking data. This extension is achieved by embedding the Mallows model within the mixtures of experts (MoE) framework, linking cluster weights to the individual respondent covariates via a generalized linear model. Specifically, individual group membership probabilities are modeled using multinomial logistic regression based on the covariates. The underlying assumption is that respondents' characteristics contribute to group formation, enhancing the characterization of preference patterns in the population compared to the standard MMS. Maximum likelihood estimation is performed through a hybrid iterative scheme combining the popular Expectation-Maximization algorithm with the Minorization-Maximization procedure. This inferential scheme benefits from two key aspects that simplify the optimization of the likelihood objective function: i) the availability of a closed-form expression for the consensus ranking estimator, related to the specific use of the Spearman metric in the Mallows model; and ii) the construction of a surrogate, more analytically tractable objective function to handle the additional estimation step of the regression coefficients. The utility of our proposal is demonstrated through applications to real-world preference ranking data.