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Estimating Finite Mixtures of Ordinal Graphical Models

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Abstract

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.

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Author notes

  1. Kevin H. Lee and Qian Chen are co-first authors who contributed equally to this paper.

Authors and Affiliations

  1. Department of Statistics, Western Michigan University, Kalamazoo, USA

    Kevin H. Lee

  2. Department of Marketing, College of Business, University of Nebraska–Lincoln, Lincoln, USA

    Qian Chen

  3. Department of Marketing, Pennsylvania State University, University Park, USA

    Wayne S. DeSarbo

  4. Department of Statistics, Pennsylvania State University, 318 Thomas Building, University Park, PA , 16802, USA

    Lingzhou Xue

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  1. Kevin H. Lee
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  4. Lingzhou Xue
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Correspondence to Lingzhou Xue.

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The authors wish to recognize and thank the Co-Editors, the Associate Editor, and three anonymous referees for their insightful and constructive comments.

The work of Lingzhou Xue was supported in part by the National Science Foundation (NSF) Grants DMS-1811552, DMS-1953189, and CCF-2007823.

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Lee, K.H., Chen, Q., DeSarbo, W.S. et al. Estimating Finite Mixtures of Ordinal Graphical Models. Psychometrika 87, 83–106 (2022). https://doi.org/10.1007/s11336-021-09781-2

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