Wu Jianmin, Bentler Peter M
Beijing Institute of Technology.
Comput Stat Data Anal. 2013 Jan;57(1):392-403. doi: 10.1016/j.csda.2012.06.022. Epub 2012 Jul 2.
Based on the Bayes modal estimate of factor scores in binary latent variable models, this paper proposes two new limited information estimators for the factor analysis model with a logistic link function for binary data based on Bernoulli distributions up to the second and the third order with maximum likelihood estimation and Laplace approximations to required integrals. These estimators and two existing limited information weighted least squares estimators are studied empirically. The limited information estimators compare favorably to full information estimators based on marginal maximum likelihood, MCMC, and multinomial distribution with a Laplace approximation methodology. Among the various estimators, Maydeu-Olivares and Joe's (2005) weighted least squares limited information estimators implemented with Laplace approximations for probabilities are shown in a simulation to have the best root mean square errors.
基于二元潜在变量模型中因子得分的贝叶斯模态估计，本文针对基于伯努利分布的二元数据、具有逻辑链接函数的因子分析模型，提出了两种新的有限信息估计量，这些估计量具有二阶和三阶的最大似然估计以及对所需积分的拉普拉斯近似。对这些估计量和两个现有的有限信息加权最小二乘估计量进行了实证研究。与基于边际最大似然、MCMC和具有拉普拉斯近似方法的多项分布的完全信息估计量相比，有限信息估计量具有优势。在各种估计量中，Maydeu-Olivares和Joe（2005）的加权最小二乘有限信息估计量在模拟中采用概率的拉普拉斯近似时表现出最佳的均方根误差。
