Department of Educational Psychology and Counseling, University at Albany.
Department of Educational Psychology, City University of New York.
Psychol Methods. 2017 Dec;22(4):760-778. doi: 10.1037/met0000136. Epub 2017 Mar 30.
The focus of this article is to describe Bayesian estimation, including construction of prior distributions, and to compare parameter recovery under the Bayesian framework (using weakly informative priors) and the maximum likelihood (ML) framework in the context of multilevel modeling of single-case experimental data. Bayesian estimation results were found similar to ML estimation results in terms of the treatment effect estimates, regardless of the functional form and degree of information included in the prior specification in the Bayesian framework. In terms of the variance component estimates, both the ML and Bayesian estimation procedures result in biased and less precise variance estimates when the number of participants is small (i.e., 3). By increasing the number of participants to 5 or 7, the relative bias is close to 5% and more precise estimates are obtained for all approaches, except for the inverse-Wishart prior using the identity matrix. When a more informative prior was added, more precise estimates for the fixed effects and random effects were obtained, even when only 3 participants were included. (PsycINFO Database Record
本文的重点是描述贝叶斯估计，包括先验分布的构建，并比较在单病例实验数据的多层次建模背景下，贝叶斯框架（使用弱信息先验）和最大似然（ML）框架下的参数恢复情况。在处理效果估计方面，贝叶斯估计结果与 ML 估计结果相似，而与贝叶斯框架中先验规范的函数形式和信息量大小无关。在方差分量估计方面，当参与者数量较少（即 3 人）时，ML 和贝叶斯估计过程都会导致偏差和不精确的方差估计。通过将参与者数量增加到 5 或 7，除了使用单位矩阵的逆 Wishart 先验之外，所有方法的相对偏差接近 5%，并且可以获得更精确的估计值。当添加更具信息量的先验时，即使只包含 3 个参与者，固定效应和随机效应的估计值也会更精确。（PsycINFO 数据库记录）
