ABSTRACT

Bayesian estimation of multilevel structural equation models (MLSEMs) offers advantages in terms of sample size requirements and computational feasibility, but does require careful specification of the prior distribution especially for the random effects variance parameters. The traditional “non-informative” conjugate choice of an inverse-Gamma prior with small hyperparameters has been shown time and again to be problematic. In this paper, we investigate alternative, more robust prior distributions for the doubly latent categorical multilevel model. In contrast to multilevel models without latent variables, MLSEMs have multiple random effects variance parameters both for the multilevel structure and for the latent variable structure. It is therefore even more important to construct reasonable priors for these parameters. We find that, although the robust priors outperform the traditional inverse-Gamma prior, their hyperparameters do require careful consideration.

摘要

多级结构方程模型 (MLSEM) 的贝叶斯估计在样本大小要求和计算可行性方面具有优势，但确实需要仔细指定先验分布，尤其是对于随机效应方差参数。具有小超参数的逆伽玛先验的传统“非信息性”共轭选择已经一次又一次地被证明是有问题的。在本文中，我们研究了双重潜在分类多级模型的替代性、更稳健的先验分布。与没有潜在变量的多级模型相比，MLSEM 具有多级结构和潜在变量结构的多个随机效应方差参数。因此，为这些参数构建合理的先验更为重要。我们发现，