a University of South Carolina.
b University of Barcelona.
Multivariate Behav Res. 2018 Sep-Oct;53(5):676-694. doi: 10.1080/00273171.2018.1476221. Epub 2018 Dec 30.
We argue that the definition of close fitting models should embody the notion of substantially ignorable misspecifications (SIM). A SIM model is a misspecified model that might be selected, based on parsimony, over the true model should knowledge of the true model be available. Because in applications the true model (i.e., the data generating mechanism) is unknown, we investigate the relationship between the population standardized root mean square residual (SRMR) values and various model misspecifications in factor analysis models to better understand the magnitudes of the SRMR. Summary effect sizes of misfit such as the SRMR are necessarily insensitive to some non-ignorable localized misspecifications (i.e., the presence of a few large residual correlations in large models). Localized misspecifications may be identified by examining the largest standardized residual covariance. Based on the findings, our population reference values for close fit are based on a two-index strategy: (1) largest absolute value of standardized residual covariance ≤0.10, and (2) SRMR ≤0.05× the average R of the manifest variables; for acceptable fit our values are 0.15 and 0.10× , respectively.
我们认为，紧密拟合模型的定义应该体现可忽略性误设（SIM）的概念。SIM 模型是一种误设的模型，如果基于简约性，在有真实模型的知识的情况下，它可能会被选择而不是真实模型。由于在应用中，真实模型（即数据生成机制）是未知的，我们研究了因子分析模型中总体标准化均方根残差（SRMR）值与各种模型误设之间的关系，以更好地理解 SRMR 的大小。拟合不良的综合效应大小，如 SRMR，必然对一些不可忽略的局部误设不敏感（即大模型中存在一些大的残差相关）。可以通过检查最大标准化残差协方差来识别局部误设。基于这些发现，我们将适合人群的紧密拟合的参考值基于两指标策略：（1）最大标准化残差协方差绝对值≤0.10；（2）SRMR≤0.05× 显变量的平均 R；对于可接受的拟合度，我们的值分别为 0.15 和 0.10× 。
