Functional effects models: Accounting for preference heterogeneity in panel data with machine learning

In this paper, we present a general specification for Functional Effects Models, which use Machine Learning (ML) methodologies to learn individual-specific preference parameters from socio-demographic characteristics, therefore accounting for inter-individual heterogeneity in panel choice data. We identify three specific advantages of the Functional Effects Model over traditional fixed, and random/mixed effects models: (i) by mapping individual-specific effects as a function of socio-demographic variables, we can account for these effects when forecasting choices of previously unobserved individuals (ii) the (approximate) maximum-likelihood estimation of functional effects avoids the incidental parameters problem of the fixed effects model, even when the number of observed choices per individual is small; and (iii) we do not rely on the strong distributional assumptions of the random effects model, which may not match reality. We learn functional intercept and functional slopes with powerful non-linear machine learning regressors for tabular data, namely gradient boosting decision trees and deep neural networks. We validate our proposed methodology on a synthetic experiment and three real-world panel case studies, demonstrating that the Functional Effects Model: (i) can identify the true values of individual-specific effects when the data generation process is known; (ii) outperforms both state-of-the-art ML choice modelling techniques that omit individual heterogeneity in terms of predictive performance, as well as traditional static panel choice models in terms of learning inter-individual heterogeneity. The results indicate that the FI-RUMBoost model, which combines the individual-specific constants of the Functional Effects Model with the complex, non-linear utilities of RUMBoost, performs marginally best on large-scale revealed preference panel data.