Linearly constrained regression with applications to origin-destination and migration studies
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Citation
Abstract
Data censored in terms of linear summaries such as sums, means, and linear combi- nations are commonly encountered in a number applications but specially in network and transportation studies, where only the total number of units entering or leaving a zone of interest are observed. While ubiquitous, this type of linearly censored data lacks adequate models and inferential procedures, often relying on computationally expensive methods such as expectation-maximization and/or Markov chain Monte Carlo. In this work we propose a curved exponential family to better represent lin- early constrained data and develop an efficient inferential procedure by extending a generalized linear model framework. Within this framework, we discuss alternative, more interpretable representations of design matrices that best align with linear con- straint matrices, and how to design hypothesis tests and assess goodness-of-fit. We further extend this model into a Bayesian paradigm by eliciting priors for shape pa- rameters, thus guiding the selection of latent data configurations yielding the linearly constrained data. We discuss tailored formulations of our methodology to origin- destination (OD) matrix estimation, a classic problem in transportation studies, and to more modern problems in migration studies. We demonstrate our methods in a number of small case studies in networks, OD, and migration estimation, and dis- cuss a more in-depth application to predict trip patterns in the London Underground subway system.
Description
2024
License
Attribution 4.0 International