線性混合模型與結構方程模型之比較 - 以台灣青少年成長歷程研究計畫為例

Comparing general linear mixed model and latent growth model - Example from Taiwan youth project

林昌瑋(Chang-Wei Lin)

指導教授 ： 林定香

國立臺北大學/商學院/統計學系/碩士(2012年)

摘要

線性混合模型 (linear mixed model) 和潛在成長模型 (latent growth model) 皆屬縱向資料分析的技術 , 在生醫 、 教育上有廣泛的應用 , 而結構方程模型 (structural equation model) 屬於多變量資料分析技術之一, 經過測量模式和結構模式檢定觀察變項 (observed variable) 與潛在變項(latent variable) 之間的假設關係。本研究目的為針對三模型的特色比較與解釋 , 分成四個特例模型無條件潛在成長模型 (unconditional latent growth model) 、 條件潛在成長模型 (conditional latent growth model) 、 非線性潛在成長模型 (nonlinear latent growth model) 與加入時間趨勢變數 (time-varying covariates) 情況下分別闡述模型彼此間的參數對應並對資料做估計與解釋 。我們使用 Taiwan youth project 為實例資料。 感興趣的變數是時間、 性別 、 自評健康和快樂, 我們對 6 個時間點的 1670 個觀察植, 採用混合線性模型和潛在成長曲線模型方法配適上述的四個特例模型。
結果顯示: 三個模型的參數估計沒有顯著性的差異。 意味著三種模式可以透過參數化而互通。

關鍵字

青少年成長歷程 ； 線性混合模型 ； 結構方程模型 ； 潛在成長模型

並列摘要

Linear mixed model and latent growth curve model are both techniques for longitudinal data analysis, and they are widely used in medicine and education. structural equation modeling is one of multivariate analyses, which tests the relationship between measurement and structural models through observed and latent variables.
This study will compare and explore the relationship among the three models, which can be divided into four special cases: the unconditional latent growth model, Conditional latent growth model, Nonlinear latent growth model related to time-varying covariates case. The study will demonstrate
the parameter correspondence among the models and provide estimates and explanation about the data.
We use Taiwan youth project as an empirical data. The variables of interest are time, gender, self-rated health and happiness. We fit the data with four special cases models with 1670 subjects of six time points, using
linear mixed model and latent growth curve model approach.
The result shows there are not significant difference of parameter estimates in the three models. The results implies that the three models can interflow through parametration.

並列關鍵字

Taiwan youth project ； general linear mixed Model ； latent growth curve model ； Structural equation model

參考文獻

Bauer D.J. (2003). ”Estimating Multilevel Linear Models as Structural Equation Models”, Journal of Educational and Behav-ioral Statistics, 28, 135-167.

Benner A.D. and Graham Sandra (2009). ”The Transition to High School as a Developmental Process Among Multiethnic Urban Youth”,Child Development, 80. 356-376.

Duncan T.E., Duncan S.C. and Strycker L.A. (1999). An Introduction to Latent Variable Growth Curve Modeling :Concepts, issues,and applications. Mahwah, New Jersey.

Applied Longitudinal Analysis. Wiley, USA.

Rovine M.J. and Molelaar P.C.M. (2001). ”A Structural Equations Modeling Approach to the General Linear Mixed Model”, New methods for the analysis of change 3, 67-91.