臺灣博碩士論文加值系統

潛在成長曲線模型(Latent Growth Curve Modeling，LGCM)對於縱貫研究資料的分析，已經被廣泛的使用在心理學、教育學或是生物醫學等研究領域上面。在一般的縱貫研究裡，我們會對於能觀察到的某些現象，包括行為、態度等，想了解隨著時間的改變，我們有興趣的現象是否會隨著時間改變，因此潛在成長曲線模型是用來分析重複測量的變數在不同時間點上，觀測值的起始狀態與被觀測時段間的成長或衰退率的變化情形。在本篇論文裡主要便探討了使用潛在成長曲線模型，當所蒐集到的樣本數很小的情形下，根據檢定統計量的表現來識別模式選擇的正確比率，或稱檢定力。
探究過往的學者，鮮少有對於小樣本的潛在成長曲線模型檢定統計量表現的探討，且對於模型的選擇多使用連續型變數為主的模型，於是本研究所選用的模型仍為連續型變數的模型，但對於模擬研究中所使用的影響因子設定六個影響因子：樣本數個數、截距項的變異數、斜率項變異數、斜率項平均數、截距項與斜率項的共變異數、觀察變項的個數。本研究使用過往學者(Nevitt ＆ Hancock, 2004；Bentler ＆ Yuan, 2000)在文章中所提出的檢定統計量來對於潛在成長曲線模型在小樣本下模式識別的檢定力表現。研究中使用蒙地卡羅(Monte Carlo)的模擬方法，首先模擬出所需要分析的資料，接著把資料放回研究中所設定的五個巢狀(nested)模型裡進行模擬研究來估算出各種影響因子條件下的檢定力表現。
經由本研究的模擬發現，影響模式選擇檢定力的主要因子為樣本數個數、截距項與斜率項的共變異數及觀察變項的個數。而對於本研究的統計量與選模指標之檢定力而言，BIC選模指標的表現最好，其次為 的表現較好，Adjusted-BIC的表現最差。最後本研究整理出可供實證研究者參考使用的檢定力表。

The use of Latent Growth Curve Modeling(LGCM), in longitudinal study data analysis has been widely used in the field of Psychology, Education and Medical research. We are interested in observing the effect of time on the action or attitude of the subject in a general longitudinal study, whether these behavior vary as time progress. Hence, LGCM is a technique to analyze the repeat measurements of a variable at different time frame. This essay will discuss the use of LGCM with small sample size, to identify the accuracy of model selection or power using test statistics.
In the past, researchers rarely investigate the use of LGCM with small sample size, and the model selection is mainly continues variable type. This research will follow the selection of model and use continues variable type. In the simulation study, the following six factors are used: number of sample sizes, variance of intercept, variance of slope, means of slope, covariance of intercept and slope, number of observation variables. This research uses the test statistics to identify the power performance of LGCM in small sample size. The research uses Monte Carlo simulation, first simulating the data need for analysis, then feedback the data in to the five nested model for simulation research to estimate the power performance in different affecting factor variation.
The results of simulation indicate that the main factors are number of sample sizes, covariance of intercept and slope and the number of observation variables. In terms of the power of the sample size and model selection for this research, BIC model selection indicator has the best performance, followed by , Adjusted-BIC has the worst performance. This research has resulted in producing a power table for the use of experimental researchers.

目錄 I
表目錄 II
圖目錄 III
第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的 2
第三節 研究貢獻 3
第二章 文獻探討 4
第一節 理論模型的介紹 4
第二節 檢定統計量與選模指標的介紹 15
第三節 影響因子之相關文獻探討 19
第三章 研究方法 21
第一節 研究設計 21
第二節 分析計畫 29
第四章 研究結果 31
第一節 影響因子研究之結果 31
第二節 多元迴歸分析結果 38
第五章 結論與建議 46
第一節 研究結論 46
第二節 研究建議與未來研究方向 47
參考文獻 49
附錄 52

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