受限制多階層潛在成長曲線模型議題探討：忽略多階層長期資料相關性之影響評估與跨階層交互作用之可能性探索

Abstract

近年來，人文社會領域大型資料庫相繼成立，其中長期資料的收集更是大型資料庫 重點所在。長期資料蘊含豐富受測者特徵變化與影響因子，但同時也潛伏相當複雜的資 料相關性：除重複量測相關性外，下層參與者資料皆非獨立存在，而是分享上層社群所 賦予的多階層相關性。忽略這類資料相關性會導致偏差的統計推論後果。相關的多階層 長期資料方法學研究卻仍相當缺乏，研究者常無所適從，或乾脆忽略長期資料裡的多階 層相關性，錯誤地探討偏頗的量化分析結果。有鑒於此，本研究案目的：因應實務研究 者分析各類「多階層長期資料庫」資料需求，提供應用於「多階層複雜性取樣長期性資 料分析」之量化研究法基礎理論與統計建模規範。本研究案專注於三個根本性問題: (1) 忽略長期資料多階層相關性，對於潛在成長曲線模型分析之影響評估、(2)忽略長期資料 多階層相關性，對於「受限制」潛在成長曲線模型分析影響評估，與 (3)在多階層長期 性資料分析內，建構跨階層交互作用之可能性探索。研究案利用數學推導與模擬實驗進 行研究，並利用實際次級多階層長期資料(如SNELS 和TEPS)證明所提建模法效果，以 將本研究案研究成果導向人文社會領域之實務長期資料分析。相關研究成果將讓國內外 實務研究者進行長期資料分析探討時，能得到精準穩健的統計分析與不偏的統計推論結 果。

Complex survey data with a hierarchical structure widely exist in social and behavioral sciences. Multilevel latent growth curve modeling (MLGCM) is a versatile tool to analyze this kind of dependent data, capture the pattern of change in repeated measures, and explore the covariate of this change. Oftentimes, researchers adopt latent growth curve models (LGCM) without considering the multilevel structure due to numerous reasons. The first and second studies of this research proposal aim to examine the influences of different model specifications using separate estimation methods on the model fit test statistics and fit indices, between/within-level estimates of regression coefficients (including the main effects and their interaction term as well), factor covariance/residual variances, and mean structures. On the other hand, when dealing with the large-scale longitudinal dataset, researchers in applied areas usually want to answer a common research question: What’s the moderation effect of individual growth patterns and demographic variables of different levels on the future outcomes? However, there is no available multivariate research methods that can help researcher to answer this question. In order to quench the thirst of researchers and explore the information of dataset, the third part of the proposal aims to explore the possibility to construct a cross-level latent interaction term in the MLGCM. I will use mathematical derivation and Monte Carlo simulations to conduct the three proposed studies. The nation-wide longitudinal databases (e.g. SNELS and TEPS) will be used to empirically demonstrate the effectiveness of the proposed models. Discussion and limitation of the studies will be provided in the midterm and final reports.