Jobst Lisa J, Auerswald Max, Moshagen Morten
Institute of Psychology and Education, Ulm University, Ulm, Germany.
Educ Psychol Meas. 2022 Oct;82(5):911-937. doi: 10.1177/00131644211046201. Epub 2021 Sep 20.
Prior studies investigating the effects of non-normality in structural equation modeling typically induced non-normality in the indicator variables. This procedure neglects the factor analytic structure of the data, which is defined as the sum of latent variables and errors, so it is unclear whether previous results hold if the source of non-normality is considered. We conducted a Monte Carlo simulation manipulating the underlying multivariate distribution to assess the effect of the source of non-normality (latent, error, and marginal conditions with either multivariate normal or non-normal marginal distributions) on different measures of fit (empirical rejection rates for the likelihood-ratio model test statistic, the root mean square error of approximation, the standardized root mean square residual, and the comparative fit index). We considered different estimation methods (maximum likelihood, generalized least squares, and (un)modified asymptotically distribution-free), sample sizes, and the extent of non-normality in correctly specified and misspecified models to investigate their performance. The results show that all measures of fit were affected by the source of non-normality but with varying patterns for the analyzed estimation methods.
先前研究结构方程模型中非正态性影响时，通常在指标变量中引入非正态性。此过程忽略了数据的因子分析结构，该结构被定义为潜在变量和误差之和，因此如果考虑非正态性的来源，之前的结果是否成立尚不清楚。我们进行了蒙特卡罗模拟，操纵潜在的多元分布，以评估非正态性来源（潜在、误差以及具有多元正态或非正态边缘分布的边缘条件）对不同拟合度量（似然比模型检验统计量的经验拒绝率、近似均方根误差、标准化均方根残差和比较拟合指数）的影响。我们考虑了不同的估计方法（最大似然法、广义最小二乘法和（未）修正的渐近分布自由法）、样本量以及正确设定和错误设定模型中的非正态程度，以研究它们的性能。结果表明，所有拟合度量都受到非正态性来源的影响，但分析的估计方法呈现出不同的模式。
