Institute of Human Resource Management, College of Management, National Sun Yat-sen University, 70 Lienhai Rd, Kaohsiung, 80424, Taiwan.
Behav Res Methods. 2021 Oct;53(5):2191-2213. doi: 10.3758/s13428-021-01547-z. Epub 2021 Mar 31.
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.
在社会和行为科学中，混合尺度类型的观测变量（即连续和分类观测变量）长期以来一直被包含在结构方程模型中。然而，对于混合连续和分类观测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估计方法，即稳健最大似然（MLR）和对角加权最小二乘法（DWLS），当分析混合连续和分类观测数据时，评估 DWLS 和 MLR 估计在测量和全结构方程模型中的行为。通过蒙特卡罗模拟，检查 DWLS 和 MLR 估计模型参数、标准误差和卡方统计量的性能。使用两种总体模型，即相关三因子测量模型和五因子结构方程模型，结合 36 种其他实验条件进行测试，这些实验条件的特征是观测变量的类别数（2、3、4、5、6 和 7）、分类观测分布形状（对称和轻微不对称）和样本量（200、500 和 1000）。使用 Mplus 8 进行数据生成和分析。结果表明：（1）对于分类观测变量，DWLS 比 MLR 产生更准确的因子负荷估计，而 DWLS 和 MLR 对连续观测变量产生可比的因子负荷估计；（2）在几乎所有条件下，DWLS 和 MLR 都能很好地估计因子间相关性和结构路径；（3）在几乎所有条件下，通过 MLR 获得的参数估计的稳健标准误差都比 DWLS 稍准确，但一旦使用中等或大样本（即 n=500 或 1000），MLR 相对于 DWLS 的优势并不明显；（4）DWLS 在控制 I 类错误率方面系统地优于 MLR，但随着样本量的增加，这种优势会减弱。文章最后对研究结果进行了一般性讨论，并就实践和未来研究提出了一些建议。
