A Hierarchical Bayesian Model With Correlated Residuals for Investigating Stability and Change in Intensive Longitudinal Data Settings
A Hierarchical Bayesian Model With Correlated Residuals for Investigating Stability and Change in Intensive Longitudinal Data Settings
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DOI：
10.1027/1614-2241/a000083
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发表时间：
2014-01-01
影响因子：
3.1
通讯作者：
Hueluer, Gizem
中科院分区：
文献类型：
--
作者：
Gasimova, Fidan;Robitzsch, Alexander;Hueluer, Gizem
本文的重点是纵向数据中个体间和个体内变异性的建模。我们提出了一个具有相关残差的分层贝叶斯模型，采用自回归参数AR（1）来关注个体内变异。分层模型具有四个个体随机效应：截距、斜率、变异性和自相关性。在三种不同样本量（N = 100，200，500）和三种不同测量点数（T = 10，20，40）的模拟纵向数据中研究了所提出的贝叶斯估计的性能。初始模拟值的选取依据的是九年级学生工作记忆容量纵向研究的前20次测量结果。在这项模拟研究中，我们调查的均方根误差（RMSE），偏差，相对百分比偏差，和90%的覆盖概率的参数估计。结果表明，更准确的估计与更大的样本量。这种趋势的一个例外是自相关参数，它对时间点数量的增加表现出更高的敏感性。
The present paper's focus is the modeling of interindividual and intraindividual variability in longitudinal data. We propose a hierarchical Bayesian model with correlated residuals, employing an autoregressive parameter AR(1) for focusing on intraindividual variability. The hierarchical model possesses four individual random effects: intercept, slope, variability, and autocorrelation. The performance of the proposed Bayesian estimation is investigated in simulated longitudinal data with three different sample sizes (N = 100, 200, 500) and three different numbers of measurement points (T = 10, 20, 40). The initial simulation values are selected according to the results of the first 20 measurement occasions from a longitudinal study on working memory capacity in 9th graders. Within this simulation study, we investigate the root mean square error (RMSE), bias, relative percentage bias, and the 90% coverage probability of parameter estimates. Results indicate that more accurate estimates are associated with a larger sample size. One exception to this tendency is the autocorrelation parameter, which shows more sensitivity to an increasing number of time points.