Department of Psychological Research Methods, Institute of Psychology and Education, Ulm University, Albert-Einstein-Allee 47, 89081, Ulm, Germany.
Behav Res Methods. 2022 Oct;54(5):2351-2363. doi: 10.3758/s13428-021-01729-9. Epub 2022 Jan 10.
In structural equation modeling, several corrections to the likelihood-ratio model test statistic have been developed to counter the effects of non-normal data. Previous robustness studies investigating the performance of these corrections typically induced non-normality in the indicator variables. However, non-normality in the indicators can originate from non-normal errors or non-normal latent factors. We conducted a Monte Carlo simulation to analyze the effect of non-normality in factors and errors on six different test statistics based on maximum likelihood estimation by evaluating the effect on empirical rejection rates and derived indices (RMSEA and CFI) for different degrees of non-normality and sample sizes. We considered the uncorrected likelihood-ratio model test statistic and the Satorra-Bentler scaled test statistic with Bartlett correction, as well as the mean and variance adjusted test statistic, a scale-shifted approach, a third moment-adjusted test statistic, and an approach drawing inferences from the relevant asymptotic chi-square mixture distribution. The results indicate that the values of the uncorrected test statistic-compared to values under normality-are associated with a severely inflated type I error rate when latent variables are non-normal, but virtually no differences occur when errors are non-normal. Although no general pattern regarding the source of non-normality for all analyzed measures of fit can be derived, the Satorra-Bentler scaled test statistic with Bartlett correction performed satisfactorily across conditions.
在结构方程建模中，已经开发了几种修正似然比模型检验统计量的方法，以抵消非正态数据的影响。以前的稳健性研究调查了这些修正方法的性能，通常会在指标变量中引入非正态性。然而，指标的非正态性可能源于非正态误差或非正态潜在因素。我们进行了一项蒙特卡罗模拟，通过评估不同程度的非正态性和样本大小对六种不同基于最大似然估计的测试统计量的影响，来分析因素和误差的非正态性对经验拒绝率和衍生指数（RMSEA 和 CFI）的影响。我们考虑了未修正的似然比模型检验统计量和带有巴特莱特校正的 Satorra-Bentler 缩放检验统计量，以及均值和方差调整检验统计量、比例调整方法、第三矩调整检验统计量和从相关渐近卡方混合分布中进行推断的方法。结果表明，当潜在变量非正态时，未修正检验统计量的值（与正态情况下的值相比）与严重膨胀的 I 型错误率相关，但当误差非正态时，几乎没有差异。虽然对于所有分析的拟合度度量，无法得出关于非正态性来源的一般模式，但带有巴特莱特校正的 Satorra-Bentler 缩放检验统计量在各种条件下表现良好。
