Hostname: page-component-669899f699-ggqkh Total loading time: 0 Render date: 2025-04-27T02:22:33.367Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  01 January 2025

Yanling Li Open the ORCID record for Yanling Li [Opens in a new window] ,
Zita Oravecz ,
Shuai Zhou ,
Yosef Bodovski ,
Ian J. Barnett ,
Guangqing Chi ,
Yuan Zhou ,
Naomi P. Friedman ,
Scott I. Vrieze  and
Sy-Miin Chow
Yanling Li*
Affiliation:
The Pennsylvania State University
Zita Oravecz
Affiliation:
The Pennsylvania State University
Shuai Zhou
Affiliation:
The Pennsylvania State University
Yosef Bodovski
Affiliation:
The Pennsylvania State University
Ian J. Barnett
Affiliation:
University of Pennsylvania
Guangqing Chi
Affiliation:
The Pennsylvania State University
Yuan Zhou
Affiliation:
University of Minnesota
Naomi P. Friedman
Affiliation:
University of Colorado Boulder
Scott I. Vrieze
Affiliation:
University of Minnesota
Sy-Miin Chow
Affiliation:
The Pennsylvania State University
*
Correspondence should be made to Yanling Li, Department of Agricultural Economics, Sociology, and Education, The Pennsylvania State University, PA 16802, State College, USA. Email: yxl823@psu.edu
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

Bayesian zero-inflated Poisson modelforecastintensive longitudinal dataregime-switchingspatial datasubstance use
Type
Theory and Methods
Information
Psychometrika , Volume 87 , Issue 2: Special Issue on Forecasting with Intensive Longitudinal Data , June 2022 , pp. 376 - 402
Copyright
Copyright © 2022 The Author(s) under exclusive licence to The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Arminger, G. (1986). Linear stochastic differential equation models for panel data with unobserved variables. Sociological Methodology, 16, 187– 212. CrossRefGoogle Scholar
Berry, L. R., & West, M. (2020). Bayesian forecasting of many count-valued time series. Journal of Business and Economic Statistics, 38 (4), 872– 887. CrossRefGoogle Scholar
Bradley, A. P. (1997). The use of the area under the ROC curve in the evaluation of machine learning algorithms. Pattern Recognition, 30 (7), 1145– 1159. CrossRefGoogle Scholar
Bronfenbrenner, U. (1992). Ecological systems theory. Jessica Kingsley Publishers.Google Scholar
Byrnes, H. F., Miller, B. A., Morrison, C. N., Wiebe, D. J., Remer, L. G., & Wiehe, S. E. (2016). Brief report: Using global positioning system (GPS) enabled cell phones to examine adolescent travel patterns and time in proximity to alcohol outlets. Journal of Adolescence, 50, 65– 68. CrossRefGoogle ScholarPubMed
Byrnes, H. F., Miller, B. A., Morrison, C. N., Wiebe, D. J., Woychik, M., & Wiehe, S. E. (2017). Association of environmental indicators with teen alcohol use and problem behavior: Teens’ observations vs. objectively-measured indicators. Health and Place, 43, 151–157.CrossRefGoogle Scholar
Cao, H., Li, X. -L., Woon, D. Y. -K., & Ng, S. -K. (2013). Integrated oversampling for imbalanced time series classification. IEEE Transactions on Knowledge and Data Engineering, 25 (12), 2809– 2822. CrossRefGoogle Scholar
Chawla, N. V., Bowyer, K. W., Hall, L. O., & Kegelmeyer, W. P. (2002). SMOTE: Synthetic minority over-sampling technique. Journal of Artificial Intelligence Research, 16, 321– 357. CrossRefGoogle Scholar
Chow, S. -M. (2019). Practical tools and guidelines for exploring and fitting linear and nonlinear dynamical systems models. Multivariate Behavioral Research, 54 (5), 690– 718. CrossRefGoogle ScholarPubMed
Chow, S. -M., Witkiewitz, K., Grasman, R. P. P. P., Maisto, S. A. (2015). The cusp catastrophe model as cross-sectional and longitudinal mixture structural equation models. Psychological Methods, 20, 142– 164. CrossRefGoogle ScholarPubMed
Chow, S. -M., & Zhang, G. (2013). Nonlinear regime-switching state-space (RSSS) models. Psychometrika Application Reviews and Case Studies, 78 (4), 740– 768. Google ScholarPubMed
Cudeck, R., & Browne, M. W. (1983). Cross-validation of covariance structures. Multivariate Behavior Research, 18, 147– 167. CrossRefGoogle ScholarPubMed
De Jong, P. (1988). A cross-validation filter for time series models. Biometrika, 75, 594– 600. CrossRefGoogle Scholar
Elkan, C. (2001). The foundations of cost-sensitive learning. In International joint conference on artificial intelligence (Vol .17, pp. 973–978).Google Scholar
Ester, M., Kriegel, H. -P., Sander, J., & Xu, X. (1996). A density-based algorithm for discovering clusters in large spatial databases with noise. Kdd (Vol 96, pp. 226–231).Google Scholar
Gelfand, A. E., Dey, D. K. & Chang, H. (1992). Model determination using predictive distributions with implementation via sampling-based methods. Bayesian Statistics 4 (p. 147–159). Oxford University Press.CrossRefGoogle Scholar
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis, New York: CRC Press. CrossRefGoogle Scholar
Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6 (6), 721– 741. CrossRefGoogle ScholarPubMed
Geng, Y., & Luo, X. (2019). Cost-sensitive convolutional neural networks for imbalanced time series classification. Intelligent Data Analysis, 23 (2), 357– 370. CrossRefGoogle Scholar
Hahsler, M., Piekenbrock, M., & Doran, D. (2019). dbscan: Fast density-based clustering with R. Journal of Statistical Software, 25, 409– 416. Google Scholar
Hall, D. B. (2000). Zero-inflated Poisson and binomial regression with random effects: A case study. Biometrics, 56 (4), 1030– 1039. CrossRefGoogle ScholarPubMed
Hamilton, J. D. (1994). Time series analysis (Vol. 2). Princeton New Jersey.Google Scholar
Hanley, J. A., & McNeil, B. J. (1982). The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology, 143 (1), 29– 36. CrossRefGoogle Scholar
Harvey, A. C. (2001). Forecasting, structural time series models and the Kalman filter, Cambridge: Cambridge University Press. Google Scholar
Helske, J. (2017). KFAS: Exponential family state space models in R. Journal of Statistical Software, 78 (10), 1– 39. CrossRefGoogle Scholar
Howard, A. L., Patrick, M. E., & Maggs, J. L. (2015). College student affect and heavy drinking: Variable associations across days, semesters, and people. Psychology of Addictive Behaviors, 29 (2), 430 CrossRefGoogle ScholarPubMed
Jacobson, N. C., Chow, S. -M., & Newman, M. G. (2019). The differential time-varying effect model (DTVEM): Identifying optimal time lags in intensive longitudinal data. Behavioral Research Methods, 51 (1), 295– 315. 10.3758/s13428-018-1101-0 CrossRefGoogle ScholarPubMed
James, P., Berrigan, D., Hart, J. E., Hipp, J. A., Hoehner, C. M., Kerr, J., & Laden, F. (2014). Effects of buffer size and shape on associations between the built environment and energy balance. Health and Place, 27, 162– 170. CrossRefGoogle ScholarPubMed
Jane-Llopis, E., & Matytsina, I. (2006). Mental health and alcohol, drugs and tobacco: A review of the comorbidity between mental disorders and the use of alcohol, tobacco and illicit drugs. Drug and Alcohol Review, 25 (6), 515– 536. CrossRefGoogle ScholarPubMed
Ji, L., Chen, M., Oravecz, Z., Cummings, E. M., Lu, Z. -H., & Chow, S. -M. (2020). A Bayesian vector autoregressive model with nonignorable missingness in dependent variables and covariates: Development, evaluation, and application to family processes. Structural Equation Modeling: A Multidisciplinary Journal, 27 (3), 442– 467. CrossRefGoogle ScholarPubMed
Kim, C. -J., & Nelson, C. R. (1999). State-space models with regime switching: classical and Gibbs-sampling approaches with applications. MIT Press Books.CrossRefGoogle Scholar
Kuiper, R. M., & Ryan, O. (2018). Drawing conclusions from cross-lagged relationships: Re-considering the role of the time-interval. Structural Equation Modeling: A Multidisciplinary Journal, 25 (5), 809– 823. CrossRefGoogle Scholar
Kuppens, P., Allen, N. B., & Sheeber, L. B. (2010). Emotional inertia and psychological maladjustment. Psychological Science, 21 (7), 984– 991. CrossRefGoogle ScholarPubMed
Lambert, D. (1992). Zero-inflated poisson regression, with an application to defects in manufacturing. Technometrics, 34 (1), 1– 14. CrossRefGoogle Scholar
Lee, A. H., Wang, K., Scott, J. A., Yau, K. K., & McLachlan, G. J. (2006). Multi-level zero-inflated Poisson regression modelling of correlated count data with excess zeros. Statistical Methods in Medical Research, 15 (1), 47– 61. CrossRefGoogle ScholarPubMed
Li, Y., Ji, L., Oravecz, Z., Brick, T. R., Hunter, M. D., & Chow, S. -M. (2019). dynr.mi: An R program for multiple imputation in dynamic modeling. International Journal of Computer Electrical Automation Control and Information Engineering. 13(5), 302–311.Google Scholar
Li, Y., Wood, J., Ji, L., Chow, S. -M., & Oravecz, Z. (2021). Fitting multilevel vector autoregressive models in Stan, JAGS, and Mplus. Structural Equation Modeling A Multidisciplinary Journal, 5, 1– 24. Google Scholar
Litt, M. D., Cooney, N. L., & Morse, P. (1998). Ecological momentary assessment (EMA) with treated alcoholics: Methodological problems and potential solutions. Health Psychology, 17 (1), 48 CrossRefGoogle ScholarPubMed
Little, R. J. A, & Rubin, D. B. (1987). Statistical analysis with missing data, New York: Wiley. Google Scholar
Lu, Z. -H., Chow, S. -M., Ram, N., & Cole, P. M. (2019). Zero-inflated regime-switching stochastic differential equation models for highly unbalanced multivariate, multi-subject time-series data. Psychometrika, 84 (2), 611– 645. CrossRefGoogle ScholarPubMed
Lu, Z. -H., Chow, S. -M., Sherwood, A., & Zhu, H. (2015). Bayesian analysis of ambulatory cardiovascular dynamics with application to irregularly spaced sparse data. Annals of Applied Statistics, 9, 1601– 1620. CrossRefGoogle ScholarPubMed
Lütkepohl, H. (2005). Introduction to multiple time series analysis, 2 New York: Springer-Verlag. CrossRefGoogle Scholar
MacCallum, R. C., Roznowski, M., Mar, C. M., & Reith, J. V. (1994). Alternative strategies for cross-validation of covariance structure models. Multivariate Behavioral Research, 29 (1), 1– 32. CrossRefGoogle ScholarPubMed
Maisto, S. A., Xie, F. C., Witkiewitz, K., Ewart, C. K., Connors, G. J., Zhu, H., & Chow, S. -M. (2017). How chronic self-regulatory stress, poor anger regulation, and momentary affect undermine treatment for alcohol use disorder: Integrating social action theory and the dynamic model of relapse. Journal of Social and Clinical Psychology, 36, 238– 263. CrossRefGoogle Scholar
Min, Y., & Agresti, A. (2005). Random effect models for repeated measures of zero-inflated count data. Statistical Modelling, 5 (1), 1– 19. CrossRefGoogle Scholar
Moniz, N., Branco, P., & Torgo, L. (2017). Resampling strategies for imbalanced time series forecasting. International Journal of Data Science and Analytics, 3 (3), 161– 181. CrossRefGoogle Scholar
Neal, R. M. (2003). Slice sampling. Annals of Statistics, 31 (3), 705– 741. CrossRefGoogle Scholar
Neelon, B. H., O’Malley, A. J., & Normand, S. -L. T. (2010). A Bayesian model for repeated measures zero-inflated count data with application to outpatient psychiatric service use. Statistical Modelling, 10(4), 421–439.CrossRefGoogle Scholar
Oravecz, Z., Tuerlinckx, F., & Vandekerckhove, J. (2011). A hierarchical latent stochastic differential equation model for affective dynamics. Psychological Methods, 16 (4), 468 CrossRefGoogle ScholarPubMed
Orrù, G., Monaro, M., Conversano, C., Gemignani, A., & Sartori, G. (2020). Machine learning in psychometrics and psychological research. Frontiers in Psychology, 10, 2970 CrossRefGoogle ScholarPubMed
Oud, J. H., & Jansen, R. A. (2000). Continuous time state space modeling of panel data by means of SEM. Psychometrika, 65 (2), 199– 215. CrossRefGoogle Scholar
Pasch, K. E., Hearst, M. O., Nelson, M. C., Forsyth, A., & Lytle, L. A. (2009). Alcohol outlets and youth alcohol use: Exposure in suburban areas. Health and Place, 15 (2), 642– 646. CrossRefGoogle ScholarPubMed
Perchoux, C., Chaix, B., Brondeel, R., & Kestens, Y. (2016). Residential buffer, perceived neighborhood, and individual activity space: New refinements in the definition of exposure areas-the RECORD Cohort Study. Health and Place, 40, 116– 122. CrossRefGoogle ScholarPubMed
Piironen, J., & Vehtari, A. (2017). Comparison of Bayesian predictive methods for model selection. Statistics and Computing, 27 (3), 711– 735. CrossRefGoogle Scholar
Plummer, M., et al. (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd international workshop on distributed statistical computing (Vol. 124, pp. 1-10).Google Scholar
Reboussin, B. A., Song, E. -Y., & Wolfson, M. (2011). The impact of alcohol outlet density on the geographic clustering of underage drinking behaviors within census tracts. Alcoholism Clinical and Experimental Research, 35 (8), 1541– 1549. Google ScholarPubMed
Roychoudhury, S., Ghalwash, M., & Obradovic, Z. (2017). Cost sensitive time-series classification. In Joint European conference on machine learning and knowledge discovery in databases (pp. 495–511).CrossRefGoogle Scholar
Russell, M. A., Almeida, D. M., & Maggs, J. L. (2017). Stressor-related drinking and future alcohol problems among university students. Psychology of Addictive Behaviors, 31 (6), 676 CrossRefGoogle ScholarPubMed
Russell, M. A., & Odgers, C. L. (2020). Adolescents’ subjective social status predicts day-to-day mental health and future substance use. Journal of Research on Adolescence, 30, 532–544.CrossRefGoogle Scholar
Sánchez-Sánchez, P. A., García-González, J. R., & Coronell, L. H. P. (2019). Encountered problems of time series with neural networks: Models and architectures. IntechOpen: In Recent trends in artificial neural networks-from training to prediction.Google Scholar
Shen, H. (2010). Exponentially weighted methods for forecasting intraday time series with multiple seasonal cycles: Comments. International Journal of Forecasting, 26, 653– 654. CrossRefGoogle Scholar
Substance Abuse and Mental Health Services Administration, Office of Applied Studies. (2008). Results from the 2007 National Survey on Drug Use and Health: National Findings (DHHS Publication No. SMA 08-4343, NSDUH Series H-34). Rockville, MD: Substance Abuse and Mental Health Services Administration.Google Scholar
Vehtari, A., Gelman, A., & Gabry, J. (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing, 27 (5), 1413– 1432. CrossRefGoogle Scholar
Voelkle, M. C., Oud, J. H., Davidov, E., & Schmidt, P. (2012). An SEM approach to continuous time modeling of panel data: Relating authoritarianism and anomia. Psychological Methods, 17 (2), 176 CrossRefGoogle ScholarPubMed
West, M., & Harrison, J. (1997). Bayesian forecasting and dynamic models, 2 New York: Springer-Verlag. Google Scholar
Wilhelm, F. H., Grossman, P., & Muller, M. I. (2012). Bridging the gap between the laboratory and the real world: Integrative ambulatory psychophysiology. In Handbook of research methods for studying daily life (pp. 210–234). Guilford: New York.Google Scholar
Wray, T. B., Merrill, J. E., & Monti, P. M. (2014). Using ecological momentary assessment (EMA) to assess situation-level predictors of alcohol use and alcohol-related consequences. Alcohol Research: Current Reviews, 36 (1), 19– Google ScholarPubMed
Yarkoni, T., & Westfall, J. (2017). Choosing prediction over explanation in psychology: Lessons from machine learning. Perspectives on Psychological Science, 12 (6), 1100– 1122. CrossRefGoogle ScholarPubMed
Yau, K. K., & Lee, A. H. (2001). Zero-inflated Poisson regression with random effects to evaluate an occupational injury prevention programme. Statistics in Medicine, 20 (19), 2907– 2920. CrossRefGoogle ScholarPubMed
You, D., Hunter, M., Chen, M., & Chow, S. -M. (2019). A diagnostic procedure for detecting outliers in linear state-space models. Multivariate Behavioral Research, (PMID: 31264463) Google ScholarPubMed
Zhou, S., Li, Y., Bodovski, Y., Chi, G., & Chow, S.-M. (2021a). GPS2space: An open-source Python library for spatial data building and spatial measure extraction. https://github.com/shuai-zhou/gps2space. https://doi.org/10.5281/zenodo.4672651.CrossRefGoogle Scholar
Zhou, S., Li, Y., Chi, G., Yin, J., Oravecz, Z., Bodovski, Y., ... & Chow, S. M. (2021b). GPS2space: an open-source Python library for spatial measure extraction from GPS data. Journal of Behavioral Data Science, 1(2), 127–155.CrossRefGoogle Scholar