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系統識別號 U0026-0608201215095500
論文名稱(中文) 成長曲線模式之樣本單位數決定研究:蒙地卡羅模擬
論文名稱(英文) Determining Sample Sizes for Growth Curve Modeling: A Monte Carlo Simulation
校院名稱 成功大學
系所名稱(中) 教育研究所
系所名稱(英) Graduate Institute of Education
學年度 100
學期 2
出版年 101
研究生(中文) 巫博瀚
研究生(英文) Po-Han Wu
電子信箱 pohan0514@gmail.com
學號 U38961026
學位類別 博士
語文別 中文
論文頁數 63頁
口試委員 召集委員-劉湘川
口試委員-吳裕益
口試委員-許清芳
口試委員-鄭中平
指導教授-陸偉明
中文關鍵字 多層次模式  成長曲線模式  樣本數決定  蒙地卡羅模擬研究 
英文關鍵字 multilevel modeling  growth curve modeling  determining sample sizes  Monte Carlo simulation study 
學科別分類
中文摘要 近年來多層次模式已成為縱貫或重複測量資料的主流分析方式。然而,在進行成長曲線模式分析時,不同層次的模式需要多大的樣本方足以獲得不偏的參數估計結果,迄今尚無模擬研究予以探討。因此,各層所需的樣本數如何配置,向為進行縱貫性調查研究的重大挑戰,其重要性日益殷切。
為釐清前述研究議題,本研究以縱貫研究常見的樣本配置組合為模擬設計依據,期透過蒙地卡羅模擬研究,探討不同樣本規模與二層配置對於無條件成長模式與條件成長模式參數估計值(迴歸係數)與隨機效果變異數正確性的影響,並依據模擬研究結果提出最有效率的樣本數配置組合。本研究操弄的影響因子為「每一個人的時點數」與「人數」,並使用Mplus5.21版統計軟體進行內部蒙地卡羅模擬研究,模擬資料的產生與分析均透過Mplus的MONTECARLO指令進行分析,估計方法採ML估計法。
研究結果發現,無論是無條件成長模式或條件成長模式,當第二層分析單位數達100或100人以上時,無論第一層的分析單位數(波數)為三波、四波、五波或六波,對於迴歸係數的估計都是不偏的。此外,當第二層的樣本規模(人數)較小時,則隨機效果的估計會有嚴重的偏誤,而當提高第二層分析單位的樣本規模時,則隨機效果參數的估計將會愈正確。總括來說,如果研究者只關心模式中的固定效果時,則使用小規模樣本(100人)即能獲得良好的估計,然而當研究者亦關注模式中的隨機效果時,則無可避免地必須使用較大規模的樣本,方能滿足參數估計正確性的要求。
英文摘要 Multilevel modeling has become the main methodology for analyzing longitudinal or repeated measures data recently. Moreover, determining the required sample size at different levels is the important issue for longitudinal studies. However, few simulation study discusses the required sample size to gain unbiased estimated parameters on growth curve modeling at different levels. This work designed Monte Carlo simulation to investigate the impacts of an unconditional growth model and those of a conditional growth model on the accuracies of estimated parameters (regression coefficients) and random effect variances, respectively. The manipulated factors were ‘the number of time points per person’ and ‘the number of people.’ All the analyses were conducted by using Mplus 5.21; simulated data were generated from the command of MONTECARLO, and then the data were estimated by ML estimation.

The results indicated that the estimated regression coefficients were unbiased in both unconditional and conditional growth models when the second level contained more than 100 units, no matter the first level unit. In addition, when the second level has a small sample (i.e., small number of people), the estimations for random effect were seriously biased. However, a larger sample had its estimations more accurately. In sum, if the researchers only discuss fixed effects in the model, a small sample (e.g., 100) in the level 2 can gain the good estimations. If the researchers focus on the random effects as well, a large sample is needed to have accurately estimated parameters
論文目次 第一章 緒論 1
第一節 研究動機 1
第二節 研究目的 5
第三節 研究的重要性 6
第二章 文獻探討 7
第一節 成長曲線模式 7
壹、成長曲線模式簡述 7
貳、以多層次分析處理縱貫資料的特色與優勢 8
參、多層次成長模式之建立 10
第二節 樣本數與估計正確性 16
壹、多層次分析的樣本數決定 16
貳、固定效果參數及其標準誤的正確性 19
參、隨機參數及其標準誤的正確性 22
肆、不同層次樣本數與估計正確性 23
伍、小結 24
第三章 研究方法 26
第一節 模擬研究設計 26
壹、研究一—無條件成長模式之模擬模式 27
貳、研究二—條件成長模式之模擬模式 28
參、研究因子 29
肆、模擬程序與相關設定 30
第二節 資料分析與評估 32
第四章 研究結果 33
第一節 無條件成長模式之模擬結果 33
壹、固定效果的估計 33
貳、隨機效果的估計 34
第二節 條件成長模式之模擬結果 44
壹、固定效果的估計 44
貳、隨機效果的估計 45
第五章 研究結論與建議 54
第一節 結論 54
第二節 建議 58
壹、實務研究建議 58
貳、未來研究方向 59
參考文獻 61
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巫博瀚、陸偉明(2012)。台灣青少年憂鬱情緒成長發展之縱貫研究:多層次分析。
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