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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.**
*(English)*
Zbl 1490.62409

Summary: 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.

### MSC:

62P15 | Applications of statistics to psychology |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62F15 | Bayesian inference |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

### Keywords:

Bayesian zero-inflated Poisson model; forecast; intensive longitudinal data; regime-switching; spatial data; substance use
Full Text:
DOI

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