Chen Rusan
Center for New Designs in Learning and Scholarship, Georgetown University, Washington, DC 20057, USA.
Behav Res Methods Instrum Comput. 2003 May;35(2):310-7. doi: 10.3758/bf03202557.
Maximum likelihood factor analysis (MLFA), originally introduced by Lawley (1940), is based on a firm mathematical foundation that allows hypothesis testing when normality is assumed with large sample sizes. MLFA has gained in popularity since Jöreskog (1967) implemented an iterative algorithm to estimate parameters. This article presents a concise program using matrix language SAS/IML with the optimization subroutine NLPQN to obtain MLFA solutions. The program is pedagogically useful because it shows the step-by-step computational processes for MLFA, whereas almost all other statistical packages for MLFA are in "black boxes." It is also demonstrated that this approach can be extended to other multivariate methods requiring numerical optimizations, such as the widely used structural equation modeling. Researchers may find this program useful in conducting Monte Carlo simulation studies to investigate the properties of multivariate methods that involve numerical optimizations.
最大似然因子分析（MLFA）最初由劳利（1940年）提出，它基于坚实的数学基础，在大样本量且假设数据呈正态分布时允许进行假设检验。自从约雷斯克（1967年）实现了一种迭代算法来估计参数后，MLFA越来越受欢迎。本文展示了一个使用矩阵语言SAS/IML以及优化子程序NLPQN来获得MLFA解的简洁程序。该程序在教学上很有用，因为它展示了MLFA的逐步计算过程，而几乎所有其他用于MLFA的统计软件包都是“黑箱”操作。还证明了这种方法可以扩展到其他需要数值优化的多元方法，比如广泛使用的结构方程建模。研究人员可能会发现这个程序在进行蒙特卡罗模拟研究以探究涉及数值优化的多元方法的性质时很有用。
