Rijmen Frank, Vansteelandt Kristof, De Boeck Paul
Clinical Epidemiology and Biostatistics, VU Medical Center, De Boelelaan 1118, 1007 MB Amsterdam, The Netherlands.
Psychometrika. 2008 Jun;73(2):167-182. doi: 10.1007/s11336-007-9001-8. Epub 2007 Oct 4.
The increasing use of diary methods calls for the development of appropriate statistical methods. For the resulting panel data, latent Markov models can be used to model both individual differences and temporal dynamics. The computational burden associated with these models can be overcome by exploiting the conditional independence relations implied by the model. This is done by associating a probabilistic model with a directed acyclic graph, and applying transformations to the graph. The structure of the transformed graph provides a factorization of the joint probability function of the manifest and latent variables, which is the basis of a modified and more efficient E-step of the EM algorithm. The usefulness of the approach is illustrated by estimating a latent Markov model involving a large number of measurement occasions and, subsequently, a hierarchical extension of the latent Markov model that allows for transitions at different levels. Furthermore, logistic regression techniques are used to incorporate restrictions on the conditional probabilities and to account for the effect of covariates. Throughout, models are illustrated with an experience sampling methodology study on the course of emotions among anorectic patients.
日记法使用的日益增加，需要开发适当的统计方法。对于由此产生的面板数据，潜在马尔可夫模型可用于对个体差异和时间动态进行建模。通过利用模型所隐含的条件独立关系，可以克服与这些模型相关的计算负担。这是通过将概率模型与有向无环图相关联，并对该图应用变换来实现的。变换后图的结构提供了显变量和潜变量联合概率函数的因式分解，这是EM算法修改后更高效的E步的基础。通过估计一个涉及大量测量场合的潜在马尔可夫模型，以及随后对允许不同水平转换的潜在马尔可夫模型进行分层扩展，来说明该方法的有效性。此外，逻辑回归技术用于纳入对条件概率的限制，并考虑协变量的影响。全文通过一项关于厌食症患者情绪过程的经验抽样方法研究对模型进行了说明。
