Graphical models have received an increasing amount of attention in network psychometrics as a promising probabilistic approach to study the conditional relations among variables using graph theory. Despite recent advances, existing methods on graphical models usually assume a homogeneous population and focus on binary or continuous variables. However, ordinal variables are very popular in many areas of psychological science, and the population often consists of several different groups based on the heterogeneity in ordinal data. Driven by these needs, we introduce the finite mixture of ordinal graphical models to effectively study the heterogeneous conditional dependence relationships of ordinal data. We develop a penalized likelihood approach for model estimation, and design a generalized expectation-maximization (EM) algorithm to solve the significant computational challenges. We examine the performance of the proposed method and algorithm in simulation studies. Moreover, we demonstrate the potential usefulness of the proposed method in psychological science through a real application concerning the interests and attitudes related to fan avidity for students in a large public university in the United States.

图形模型在网络心理测量学中受到越来越多的关注，作为一种很有前途的概率方法，可以使用图论研究变量之间的条件关系。尽管最近取得了一些进展，但现有的图形模型方法通常假设人口是同质的，并专注于二元或连续变量。然而，序数变量在心理科学的许多领域非常流行，并且基于序数数据的异质性，总体通常由几个不同的群体组成。在这些需求的驱动下，我们引入了有序图模型的有限混合，以有效地研究有序数据的异构条件依赖关系。我们开发了一种用于模型估计的惩罚似然方法，并设计一种广义期望最大化 (EM) 算法来解决重大的计算挑战。我们在模拟研究中检查了所提出的方法和算法的性能。此外，我们通过对美国一所大型公立大学学生与粉丝狂热相关的兴趣和态度的实际应用，证明了所提出的方法在心理科学中的潜在有用性。