EAST CHINA NORMAL UNIVERSITY, London, England.
Department of Statistics, London School of Economics and Political Science, London, England.
Psychometrika. 2022 Dec;87(4):1473-1502. doi: 10.1007/s11336-022-09863-9. Epub 2022 May 7.
Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of many latent variables, (2) the observed and latent variables being continuous, discrete, or a combination of both, (3) constraints on parameters, and (4) penalties on parameters to impose model parsimony. The estimation often involves maximizing an objective function based on a marginal likelihood/pseudo-likelihood, possibly with constraints and/or penalties on parameters. Solving this optimization problem is highly non-trivial, due to the complexities brought by the features mentioned above. Although several efficient algorithms have been proposed, there lacks a unified computational framework that takes all these features into account. In this paper, we fill the gap. Specifically, we provide a unified formulation for the optimization problem and then propose a quasi-Newton stochastic proximal algorithm. Theoretical properties of the proposed algorithms are established. The computational efficiency and robustness are shown by simulation studies under various settings for latent variable model estimation.
潜变量模型在心理测量学及相关领域发挥着核心作用。在许多现代应用中，基于潜变量模型的推断涉及以下一个或多个特征：（1）存在许多潜变量；（2）观测变量和潜变量是连续的、离散的或两者的组合；（3）对参数的约束；（4）对参数施加惩罚以实现模型简约。估计通常涉及最大化基于边际似然/伪似然的目标函数，可能对参数施加约束和/或惩罚。由于上述特征带来的复杂性，解决这个优化问题极具挑战性。尽管已经提出了几种有效的算法，但缺乏一个统一的计算框架来考虑所有这些特征。在本文中，我们填补了这一空白。具体来说，我们为优化问题提供了一个统一的公式，然后提出了一种拟牛顿随机逼近算法。我们建立了所提出算法的理论性质。通过在各种潜变量模型估计设置下的模拟研究，展示了算法的计算效率和鲁棒性。
