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Statistical estimation of structural equation models with a mixture of continuous and categorical observed variables
Behavior Research Methods ( IF 5.953 ) Pub Date : 2021-03-31 , DOI: 10.3758/s13428-021-01547-z
Cheng-Hsien Li

In the social and behavioral sciences, observed variables of mixed scale types (i.e., both continuous and categorical observed variables) have long been included in structural equation models. However, little is known about the impact of mixed continuous and categorical observed variables on the performance of existing estimation methods. This study compares two popular estimation methods with robust corrections, robust maximum likelihood (MLR) and diagonally weighted least squares (DWLS), when mixed continuous and categorical observed data are analyzed, evaluating the behavior of DWLS and MLR estimates in both measurement and full structural equation models. Monte Carlo simulation was carried out to examine the performance of DWLS and MLR in estimating model parameters, standard errors, and chi-square statistics. Two population models, a correlated three-factor measurement model and a five-factor structural equation model, were tested in combination with 36 other experimental conditions characterized by the number of observed variables’ categories (2, 3, 4, 5, 6, and 7), categorical observed distribution shape (symmetry and slight asymmetry), and sample size (200, 500, and 1000). Data generation and analysis were performed with Mplus 8. Results reveal that (1) DWLS yields more accurate factor loading estimates for categorical observed variables than MLR, whereas DWLS and MLR produce comparable factor loading estimates for continuous observed variables; (2) inter-factor correlations and structural paths are estimated equally well by DWLS and MLR in nearly all conditions; (3) robust standard errors of parameter estimates obtained by MLR are slightly more accurate than those produced by DWLS in almost every condition, but the superiority of MLR over DWLS is not clearly evident once a medium or large sample is used (i.e., n = 500 or 1000); and (4) DWLS is systematically superior to MLR in controlling Type I error rates, but this superiority is attenuated with increasing sample size. The article concludes with a general discussion of the findings and some recommendations for practice and future research.



中文翻译:

具有连续和分类观察变量的混合结构方程模型的统计估计

在社会和行为科学中,混合尺度类型的观察变量(即连续和分类观察变量)早已包含在结构方程模型中。然而,关于混合连续和分类观察变量对现有估计方法性能的影响知之甚少。本研究比较了两种流行的具有鲁棒校正的估计方法,鲁棒最大似然 (MLR) 和对角加权最小二乘法 (DWLS),当分析混合的连续和分类观测数据时,评估 DWLS 和 MLR 估计在测量和全结构中的行为方程模型。进行蒙特卡罗模拟以检查 DWLS 和 MLR 在估计模型参数、标准误差和卡方统计量方面的性能。两种人口模型,一个相关的三因素测量模型和一个五因素结构方程模型,结合 36 个其他实验条件进行了测试,这些实验条件以观察变量的类别数(2、3、4、5、6 和 7)为特征,分类观察到的分布形状(对称和轻微不对称)和样本大小(200、500 和 1000)。使用 M 进行数据生成和分析8. 结果表明 (1) DWLS 对分类观察变量产生的因子载荷估计比 MLR 更准确,而 DWLS 和 MLR 对连续观察变量产生可比较的因子载荷估计;(2) DWLS 和 MLR 在几乎所有条件下都能很好地估计因子间相关性和结构路径;(3) MLR 获得的参数估计的稳健标准误差几乎在所有条件下都比 DWLS 产生的准确度略高,但是一旦使用中型或大样本(即n = 500 或 1000);(4) DWLS 在控制 I 类错误率方面系统性地优于 MLR,但这种优势随着样本量的增加而减弱。文章最后对研究结果进行了一般性讨论,并对实践和未来研究提出了一些建议。

更新日期:2021-04-01
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