ABSTRACT

This paper presents a numerically more efficient implementation of the quadratic form minimum distance (MD) estimator with a fixed weight matrix for confirmatory factor analysis (CFA) models. In structural equation modeling (SEM) computer software, such as EQS, lavaan, LISREL and Mplus, various MD estimators are available to the user. Standard procedures for implementing MD estimators involve a one-step approach applying non-linear optimization techniques. Our implementation differs from the standard approach by utilizing a two-step estimation procedure. In the first step, only a subset of the parameters are estimated using non-linear optimization. In the second step, the remaining parameters are obtained using numerically efficient linear least squares (LLS) methods. Through examples, it is demonstrated that the proposed implementation of MD estimators may be considerably faster than what the standard implementation offer. The proposed procedure will be of particular interest in computationally intensive applications such as simulation, bootstrapping, and other procedures involving re-sampling.

摘要

本文提出了一种具有固定权重矩阵的二次形式最小距离 (MD) 估计器在数值上更有效的实现，用于验证性因子分析 (CFA) 模型。在结构方程建模 (SEM) 计算机软件中，例如 EQS、lavaan、LISREL 和 Mplus，用户可以使用各种 MD 估计器。实施 MD 估计器的标准程序涉及应用非线性优化技术的一步法。我们的实现与标准方法不同，它使用了一个两步估计程序。在第一步中，仅使用非线性优化来估计参数的一个子集。在第二步中，其余参数使用数值有效的线性最小二乘 (LLS) 方法获得。通过实例，结果表明，MD 估计器的建议实施可能比标准实施提供的要快得多。所提出的程序将特别关注计算密集型应用程序，例如模拟、引导和其他涉及重新采样的程序。