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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

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
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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.

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

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