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.
翻译:在很多现代应用中,基于潜在变量模型的推论涉及以下一个或几个特点:(1) 存在许多潜在变量,(2) 观察到的和潜在的变量是连续的,离散的,或两者兼而有之,(3) 对参数的限制,(4) 对实施模型皮质的参数的处罚。估计往往涉及根据边际可能性/假假可能性(可能存在制约和/或对参数的处罚)最大限度地发挥客观功能。解决这一优化问题,由于上述特征的复杂性,是高度非三重性的。虽然提出了几种有效的算法,但缺乏一个考虑到所有这些特征的统一的计算框架。在本文件中,我们填补了空白。具体地说,我们为优化问题提供了统一的配方,然后提出了准牛顿的随机分析算法。提议的算法的理论特性已经确立。计算效率和稳健性通过在各种情况下进行潜在变量模型的模拟研究得到证明。