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Bayesian Forecasting with a Regime-Switching Zero-Inflated Multilevel Poisson Regression Model: An Application to Adolescent Alcohol Use with Spatial Covariates

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Abstract

In this paper, we present and evaluate a novel Bayesian regime-switching zero-inflated multilevel Poisson (RS-ZIMLP) regression model for forecasting alcohol use dynamics. The model partitions individuals’ data into two phases, known as regimes, with: (1) a zero-inflation regime that is used to accommodate high instances of zeros (non-drinking) and (2) a multilevel Poisson regression regime in which variations in individuals’ log-transformed average rates of alcohol use are captured by means of an autoregressive process with exogenous predictors and a person-specific intercept. The times at which individuals are in each regime are unknown, but may be estimated from the data. We assume that the regime indicator follows a first-order Markov process as related to exogenous predictors of interest. The forecast performance of the proposed model was evaluated using a Monte Carlo simulation study and further demonstrated using substance use and spatial covariate data from the Colorado Online Twin Study (CoTwins). Results showed that the proposed model yielded better forecast performance compared to a baseline model which predicted all cases as non-drinking and a reduced ZIMLP model without the RS structure, as indicated by higher AUC (the area under the receiver operating characteristic (ROC) curve) scores, and lower mean absolute errors (MAEs) and root-mean-square errors (RMSEs). The improvements in forecast performance were even more pronounced when we limited the comparisons to participants who showed at least one instance of transition to drinking.

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Notes

  1. Note that in this article, the “ZI regime” and “drinking regime” were used in the context of alcohol use to correspond to the ZI and Poisson process in the ZIP model, respectively.

  2. One “drink” is equal to 1 can or bottle of beer, a glass of wine, or a shot of hard liquor.

  3. It should be noted that these Euclidean distances were crude measures and did not measure the actual road distances that the participants had to travel (by walking or transportation) to the landmarks. Future research could consider road network-based distance measures.

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Authors and Affiliations

  1. Department of Agricultural Economics, Sociology, and Education, The Pennsylvania State University, PA 16802, State College, USA

    Yanling Li, Zita Oravecz, Shuai Zhou, Yosef Bodovski, Guangqing Chi & Sy-Miin Chow

  2. Department of Biostatistics, Epidemiology, and Informatics, University of Pennsylvania, Philadelphia, USA

    Ian J. Barnett

  3. Department of Psychology, University of Minnesota, Minneapolis, USA

    Yuan Zhou & Scott I. Vrieze

  4. Department of Psychology and Neuroscience, University of Colorado Boulder, Boulder, USA

    Naomi P. Friedman

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  1. Yanling Li
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Funding for this study was provided by the NIH Intensive Longitudinal Health Behavior Cooperative Agreement Program under U24AA027684 and U01DA046413 (SV/NF), National Science Foundation grants BCS-1052736, IGE-1806874, and SES-1823633, the Eunice Kennedy Shriver National Institute of Child Health and Human Development under P2C HD041025, and the Pennsylvania State University Quantitative Social Sciences Initiative and UL TR000127 from the National Center for Advancing Translational Sciences. Part of the computations for this research were performed on the Pennsylvania State University’s Institute for Computational and Data Sciences’ Roar supercomputer.

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Li, Y., Oravecz, Z., Zhou, S. et al. Bayesian Forecasting with a Regime-Switching Zero-Inflated Multilevel Poisson Regression Model: An Application to Adolescent Alcohol Use with Spatial Covariates. Psychometrika 87, 376–402 (2022). https://doi.org/10.1007/s11336-021-09831-9

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