Modeling Drinking Behavior Progression in Youth with Cross-sectional Data: Solving an Under-identified Probabilistic Discrete Event System
Robert L. Cook,
Background: The probabilistic discrete event systems (PDES) method provides a promising
approach to study dynamics of underage drinking using cross-sectional data. However, the utility of
this approach is often limited because the constructed PDES model is often non-identifiable. The
purpose of the current study is to attempt a new method to solve the model.
Methods: A PDES-based model of alcohol use behavior was developed with four progression stages
(never-drinkers [ND], light/moderate-drinker [LMD], heavy-drinker [HD], and ex-drinker [XD])
linked with 13 possible transition paths. We tested the proposed model with data for participants aged 12-21 from the
2012 National Survey on Drug Use and Health (NSDUH). The Moore-Penrose (M-P) generalized inverse matrix method
was applied to solve the proposed model.
Results: Annual transitional probabilities by age groups for the 13 drinking progression pathways were successfully
estimated with the M-P generalized inverse matrix approach. Result from our analysis indicates an inverse “J” shape curve
characterizing pattern of experimental use of alcohol from adolescence to young adulthood. We also observed a dramatic
increase for the initiation of LMD and HD after age 18 and a sharp decline in quitting light and heavy drinking.
Conclusion: Our findings are consistent with the developmental perspective regarding the dynamics of underage drinking,
demonstrating the utility of the M-P method in obtaining a unique solution for the partially-observed PDES drinking
behavior model. The M-P approach we tested in this study will facilitate the use of the PDES approach to examine many
health behaviors with the widely available cross-sectional data.
Keywords: Behavioral model, cross-sectional data, Moore-Penrose generalized inverse matrix, non-identifiable system PDES,
transitional probability, underage drinking.
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