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Using Mixture Models with Known Class Membership to Address Incomplete Covariance Structures in Multiple-Group Growth Models

机译：使用具有已知类别成员的混合模型来解决多组增长模型中不完全的协方差结构

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摘要

Multi-group latent growth modeling in the structural equation modeling framework has been widely utilized for examining differences in growth trajectories across multiple manifest groups. Despite its usefulness, the traditional maximum likelihood estimation for multi-group latent growth modeling is not feasible when one of the groups has no response at any given data collection point, or when all participants within a group have the same response at one of the time points. In other words, multi-group latent growth modeling requires a complete covariance structure for each observed group. The primary purpose of the present study is to show how to circumvent these data problems by developing a simple but creative approach using an existing estimation procedure for growth mixture modeling. AMonte Carlo simulation study was carried out to see whether the modified estimation approach provided tangible results and to see how these results were comparable to the standard multi-group results. The proposed approach produced the results that were valid and reliable under the mentioned problematic data conditions. We also presented a real data example and demonstrated that the proposed estimation approach can be used for the chi-square difference test to check various types of measurement invariance as conducted in a standard multi-group analysis.
机译：结构方程建模框架中的多组潜在生长建模已广泛用于检查多个清单组之间的生长轨迹差异。尽管有用，但是当一组中的任何一个在任何给定的数据收集点都没有响应，或者一组中的所有参与者一次都具有相同的响应时，用于多组潜在增长建模的传统最大似然估计是不可行的点。换句话说，多组潜在生长建模要求每个观察组具有完整的协方差结构。本研究的主要目的是说明如何通过使用现有的生长混合物建模估算程序开发一种简单但具有创造性的方法来规避这些数据问题。进行了AMonte Carlo模拟研究，以查看修改后的估算方法是否提供了切实的结果，并查看了这些结果与标准多组结果的可比性。所提出的方法所产生的结果在上述有问题的数据条件下是有效且可靠的。我们还提供了一个真实的数据示例，并证明了所提出的估计方法可用于卡方差检验，以检查标准多组分析中进行的各种类型的测量不变性。

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