Tran Trung Dung, Lesaffre Emmanuel, Verbeke Geert, Duyck Joke
Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Katholieke Universiteit Leuven, Kapucijnenvoer 35, B-3000 Leuven, Belgium and Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Universiteit Hasselt, B-3590 Diepenbeek, Belgium.
Department of Oral Health Sciences, Katholieke Universiteit Leuven, Kapucijnenvoer 7, B-3000 Leuven, Belgium.
Biostatistics. 2021 Jan 28;22(1):148-163. doi: 10.1093/biostatistics/kxz021.
We propose a Bayesian latent vector autoregressive (LVAR) model to analyze multivariate longitudinal data of binary and ordinal variables (items) as a function of a small number of continuous latent variables. We focus on the evolution of the latent variables while taking into account the correlation structure of the responses. Often local independence is assumed in this context. Local independence implies that, given the latent variables, the responses are assumed mutually independent cross-sectionally and longitudinally. However, in practice conditioning on the latent variables may not remove the dependence of the responses. We address local dependence by further conditioning on item-specific random effects. A simulation study shows that wrongly assuming local independence may give biased estimates for the regression coefficients of the LVAR process as well as the item-specific parameters. Novel features of our proposal include (i) correcting biased estimates of the model parameters, especially the regression coefficients of the LVAR process, obtained when local dependence is ignored and (ii) measuring the magnitude of local dependence. We applied our model on data obtained from a registry on the elderly population in Belgium. The purpose was to examine the values of oral health information on top of general health information.
我们提出了一种贝叶斯潜在向量自回归（LVAR）模型，用于分析二元和有序变量（项目）的多变量纵向数据，将其作为少数连续潜在变量的函数。我们关注潜在变量的演变，同时考虑响应的相关结构。在这种情况下，通常假设局部独立性。局部独立性意味着，给定潜在变量，响应在横截面上和纵向都被假设为相互独立。然而，在实践中，以潜在变量为条件可能无法消除响应之间的依赖性。我们通过进一步以项目特定的随机效应为条件来解决局部依赖性问题。一项模拟研究表明，错误地假设局部独立性可能会导致LVAR过程的回归系数以及项目特定参数的估计出现偏差。我们提议的新特点包括：（i）校正当忽略局部依赖性时获得的模型参数的偏差估计，特别是LVAR过程的回归系数；（ii）测量局部依赖性的大小。我们将我们的模型应用于从比利时老年人口登记处获得的数据。目的是研究口腔健康信息相对于一般健康信息的价值。
