Erkanli A, Soyer R, Angold A
Center for Developmental Epidemiology, Department of Psychiatry and Behavioural Sciences, Duke University Medical Center, Durham, NC 27710, USA.
Stat Med. 2001 Mar 15;20(5):755-70. doi: 10.1002/sim.702.
We present non-homogeneous Markov regression models of unknown order as a means to assess the duration of autoregressive dependence in longitudinal binary data. We describe a subject's transition probability evolving over time using logistic regression models for his or her past outcomes and covariates. When the initial values of the binary process are unknown, they are treated as latent variables. The unknown initial values, model parameters, and the order of transitions are then estimated using a Bayesian variable selection approach, via Gibbs sampling. As a comparison with our approach, we also implement the deviance information criterion (DIC) for the determination of the order of transitions. An example addresses the progression of substance use in a community sample of n = 242 American Indian children who were interviewed annually four times. An extension of the Markov model to account for subject-to-subject heterogeneity is also discussed.
我们提出了未知阶数的非齐次马尔可夫回归模型，作为评估纵向二元数据中自回归依赖性持续时间的一种方法。我们使用逻辑回归模型来描述一个人的过去结果和协变量随时间变化的转移概率。当二元过程的初始值未知时，将其视为潜在变量。然后，通过吉布斯抽样，使用贝叶斯变量选择方法估计未知的初始值、模型参数和转移阶数。作为与我们方法的比较，我们还实施了偏差信息准则（DIC）来确定转移阶数。一个例子涉及对n = 242名美国印第安儿童的社区样本进行物质使用进展情况的研究，这些儿童每年接受四次访谈。还讨论了马尔可夫模型的扩展，以考虑个体间的异质性。
