Department of Psychology, University of Massachusetts Lowell, Lowell, MA, 01854, USA.
Department of Educational Studies in Psychology, Research Methodology, and Counseling, University of Alabama, Tuscaloosa, AL, 35487, USA.
Behav Res Methods. 2023 Sep;55(6):3281-3296. doi: 10.3758/s13428-022-01964-8. Epub 2022 Sep 12.
Factor mixture modeling (FMM) has been increasingly used in behavioral and social sciences to examine unobserved population heterogeneity. Covariates (e.g., gender, race) are often included in FMM to help understand the formation and characterization of latent subgroups or classes. This Monte Carlo simulation study evaluated the performance of one-step and three-step approaches to covariate inclusion across three scenarios, i.e., correct specification (study 1), model misspecification (study 2), and model overfitting (study 3), in terms of direct covariate effects on factors. Results showed that the performance of these two approaches was comparable when class separation was large and the specification of covariate effect was correct. However, one-step FMM had better class enumeration than the three-step approach when class separation was poor, and was more robust to the misspecification or overfitting concerning direct covariate effects. Recommendations regarding covariate inclusion approaches are provided herein depending on class separation and sample size. Large sample size (1000 or more) and the use of sample size-adjusted BIC (saBIC) in class enumeration are recommended.
因子混合建模 (FMM) 在行为和社会科学中被越来越多地用于检验未观察到的人群异质性。协变量（例如，性别、种族）通常被包含在 FMM 中，以帮助理解潜在子群体或类别的形成和特征。本蒙特卡罗模拟研究评估了一步法和三步法在三种情况下纳入协变量的表现，即正确的规格说明（研究 1）、模型误设定（研究 2）和模型过拟合（研究 3），就因子上的直接协变量效应而言。结果表明，当类别分离较大且协变量效应的规格说明正确时，这两种方法的性能相当。然而，当类别分离较差时，一步法 FMM 在类别枚举方面优于三步法，并且对直接协变量效应的误设定或过拟合更具鲁棒性。根据类别分离和样本量，提供了有关协变量纳入方法的建议。建议在类别枚举中使用大样本量（1000 个或更多）和样本量调整的 BIC（saBIC）。
