Factor mixture modeling (FMM) has been increasingly used to investigate unobserved population heterogeneity. This study examined the issue of covariate effects with FMM in the context of measurement invariance testing. Specifically, the impact of excluding and misspecifying covariate effects on measurement invariance testing and class enumeration was investigated via Monte Carlo simulations. Data were generated based on FMM models with (1) a zero covariate effect, (2) a covariate effect on the latent class variable, and (3) covariate effects on both the latent class variable and the factor. For each population model, different analysis models that excluded or misspecified covariate effects were fitted. Results highlighted the importance of including proper covariates in measurement invariance testing and evidenced the utility of a model comparison approach in searching for the correct specification of covariate effects and the level of measurement invariance. This approach was demonstrated using an empirical data set. Implications for methodological and applied research are discussed.

中文翻译：

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测试未观察组的测量不变性：协变量在因子混合建模中的作用

因子混合模型 (FMM) 已越来越多地用于研究未观察到的人口异质性。本研究在测量不变性检验的背景下研究了 FMM 的协变量效应问题。具体而言，通过蒙特卡罗模拟研究了排除和错误指定协变量效应对测量不变性测试和类枚举的影响。数据是基于 FMM 模型生成的，具有 (1) 零协变量效应，(2) 对潜在类别变量的协变量效应，以及 (3) 对潜在类别变量和因子的协变量效应。对于每个总体模型，拟合了排除或错误指定协变量效应的不同分析模型。结果强调了在测量不变性测试中包含适当协变量的重要性，并证明了模型比较方法在寻找协变量效应的正确规范和测量不变性水平方面的实用性。使用经验数据集证明了这种方法。讨论了方法和应用研究的意义。