Researchers frequently wish to make incremental validity claims, suggesting that a construct of interest significantly predicts a given outcome when controlling for other overlapping constructs and potential confounders. Once the significance of such an effect has been established, it is good practice to also assess and report its magnitude. In OLS regression, this is easily accomplished by calculating the change in R-squared, ΔR², between one’s full model and a reduced model that omits all but the target predictor(s) of interest. Because observed variable regression methods ignore measurement error, however, their estimates are prone to bias and inflated type I error rates. As a result, researchers are increasingly encouraged to switch from observed variable modeling conducted in the regression framework to latent variable modeling conducted in the structural equation modeling (SEM) framework. Standard SEM software packages provide overall R² measures for each outcome, yet calculation of ΔR² is not intuitive in models with latent variables. Omitting all indicators of a latent factor in a reduced model will alter the overidentifying constraints imposed on the model, affecting parameter estimation and fit. Furthermore, omitting variables in a reduced model may affect estimation under missing data, particularly when conditioning on those variables is essential to meeting the MAR assumption. In this article, I describe four approaches to calculating ΔR² in SEMs with latent variables and missing data, compare their performance via simulation, describe a set of extensions to the methods, and provide a set of R functions for calculating ΔR² in SEM.

研究人员经常希望提出增量有效性声明，这表明在控制其他重叠结构和潜在混杂因素时，感兴趣的结构可以显着预测给定的结果。一旦确定了这种影响的重要性，优良作法就是评估和报告其严重程度。在 OLS 回归中，这很容易通过计算R平方的变化来实现，Δ R ²，在一个完整的模型和一个简化的模型之间，该模型除了感兴趣的目标预测器之外，还省略了所有的预测器。然而，由于观察变量回归方法忽略了测量误差，它们的估计容易出现偏差和夸大 I 型错误率。因此，越来越鼓励研究人员从在回归框架中进行的观察变量建模转向在结构方程建模 (SEM) 框架中进行的潜在变量建模。标准 SEM 软件包为每个结果提供总体R ²测量，但计算 Δ R ²在具有潜在变量的模型中不直观。在简化模型中省略潜在因素的所有指标将改变强加于模型的过度识别约束，影响参数估计和拟合。此外，在简化模型中省略变量可能会影响缺失数据下的估计，特别是当对这些变量进行调节对于满足 MAR 假设至关重要时。在本文中，我描述了四种方法来计算Δ - [R ²与潜在变量的SEM和丢失的数据，比较通过模拟它们的性能，描述一组扩展的所述方法，和用于计算Δ提供一组R里面的函数- [R ²中扫描电镜。