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| Title: | 多層次潛在類別模型: 樣本大小的取決及區辨力和關聯度指標的建立
Multilevel Latent Class Models: Determining the Required Sample Sizes and Developing the Distinguishability and Associaiton Measures |
| Authors: | 游琇婷 |
| Contributors: | 心理系 |
| Date: | 2018-12 |
| Issue Date: | 2025-05-28 14:06:45 (UTC+8) |
| Abstract: | 在心理研究或理論中，潛在類別變項(Discrete Latent Variable)中的不同水準(Level)可用來表徵理論構念中之潛在類別。當分析資料具多層次或階層資料結構時，多層次潛在類別模型(MLCM)在群體及個體層次假設潛在類別變項來解釋資料中所觀察到的相依性。儘管MLCM 已經應用於不同領域研究的資料分析上，但此一模型的所需樣本大小的判斷原則和取決標準仍未建立；除整體樣本大小的議題之外，MLCM 的應用也需同時考量第二階層的「組數」及第一階層的「分組大小」兩因素。此外，雖MLCM 已被用於許多實徵研究，但卻沒有可用於描述潛在類別模型中單位類別間之區辨力及關連性指標。因此，本研究計畫提出一個兩年期計畫以研究MLCM 中「樣本大小的取決」及「區辨力及關聯度指標的建立」兩個重要議題。第一年計畫擬以模擬分析來研究各種條件下MLCM 得不偏參數估計值及正確模型選擇所需的樣本大小。分別在群體及個體兩層次就模型複雜性、潛在模型結構以及題數等因素進行探討，期建立對MLCM 對於樣本大小的一般原則和實驗設計建議。第二年計畫則為發展能使用於MLCM 分析中描述單位類別間之區辨力和關連性的指標。此研究計劃指標期能幫助研究者可以更詳細地描述潛在類別之間的差異和關係，進而對模型和分析結果能有更完整和詳細的描述和解釋。
Discrete latent variables are useful tools in psychological research to represent distinct latent components. Specifically, levels of discrete latent variables can be used to capture or symbolize latent categories of theoretical concepts, constructs, entities, or subgroups. The Latent Class Model (LCM) is the classical analytical approach of using the discrete latent variable to explain dependency in observed categorical responses. When analyzing data with nested data structure (e.g., students nested with classrooms), one can apply the nonparametric version of the Multilevel Latent Class Model (MLCM) to explain the systematic variation of data by assuming discrete latent variables at both the group and individual levels. Though MLCM has been demonstrated to be a useful tool in many empirical applications, the required sample size for applying the nonparametric MLCM to analyze empirical data has not been established. Therefore, it is important to establish the empirical guidelines for the MLCM regarding the sample sizes at both higher- and lower-level. In addition, though MLCM is used in many empirical studies and is proven to be a versatile tool in data analysis, but there are no available measures or indices that can be used to describe the nature of the relationship among discrete latent components. Therefore, the proposed research proposal aims to examine these two important issues in the MLCM: (1) determining the required sample sizes for MLCMs, and (2) developing the associaiton and distinguishbility measures among discrete components. For the first project, a series of simulation studies are planned to investigate the sample sizes requirement under various conditions. A series of design factors, including sample sizes at group- and individual-level, the distinctness and the complexity of the latent structure, and the number of indicators were manipulated. The results of the simulation will be evaluated by four criteria: model selection accuracy, parameter estimation bias, standard error bias and coverage rate. The goal for this project to conclude general guidelines and rule of thumb for selecting the number of groups and the number of individuals in groups when planning research that will be analyzed using MLCM. For the second project, two subprojects are proposed to answer these research questions: What measure can quantify the degree of distinguishability among discrete latent components? What measure can summarize the degrees of association between levels? The goals of subproject 1 are to investigate how to differentiate the discrete latent components assumed in MLCM and to develop measures to distinguish the latent components at separate group and individual levels. Subproject 2 is proposed to study how to define and describe the association among the latent components between the two levels of the MLCM. Subproject 2 also sought to develop a measure that can summarize the degree of association between levels. Using the developed measures of distinguishability and association, researchers can describe the differences and relationships among these latent components in greater detail. With this information, researchers can provide a comprehensive description and interpretation of the latent structure underlying the observed data. |
| Relation: | 科技部, MOST106-2410-H004-064, 106.08-107.07 |
| Data Type: | report |
| Appears in Collections: | [心理學系] 國科會研究計畫
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