臺灣博碩士論文加值系統

調查研究中的資料分析必須搭配適當的取樣權重，才能正確的推論母體的統計模式參數。本研究主要延伸蔡良庭與楊志堅（2008）及Yang與Tsai(2006)的確認性因素分析（confirmatory factor analysis, CFA）模型，以JRR、Bootstrap、ABB及RG等不同重複取樣程序，評估分層簡單隨機取樣（Str. RS）及等比率等機率取樣（PPS）及其權重計算方式對於CFA分析的參數估計值及參數估計標準誤影響。但是當調查研究為包含多階層的複雜資料結構時，Str. RS及PPS取樣設計最為研究者所使用，但卻也最常為研究者忽略這兩種設計的不同取樣權重計算方式對於參數估計的影響。
本研究以數值模擬實驗方法，評估Str. RS及PPS取樣設計及其權重計算對於參數估計的影響，並探討不同重複取樣程序的正確性及穩定性。實驗設計除了取樣設計之外，包含連續及類別資料型態、多種不同取樣數、PSU異質性及重複取樣程序。研究結果顯示不論連續或類別資料，建議採用PPS的取樣設計及其權重計算能提供較精準的參數估計。重複取樣程序部分，相較於RG方法，JRR、Bootstrap及ABB程序能提供更精準且穩定的參數估計。

In large-scale survey, appropriate sampling weights have to be engaged to ensure proper statistical inferences for population parameters. A further extension factor analysis model based on Tsai and Yang (2008) and Yang and Tsai (2006) was proposed in this study. The model was used to evaluate the effect of different resampling procedure (JRR, Bootstrap, ABB, and RG), combined with stratified random sampling (Str. RS) and probability proportional to size (PPS), on the accuracy of parameter and standard error estimation. When complex sampling data were found in survey researches, the Str. RS and PPS sampling designs are often applied. However, the effects of different sampling weights within these two designs on the parameter estimation were often neglected.
The effects of parameter estimation by using Str. RS and PPS sampling design on the accuracy were investigated through a numerical simulation study. The accuracy and stability of parameter estimate under different resampling approaches were also discussed. Independent variables that manipulated in this study includes the sampling designs, data type (continuous or categorical), sampling size, variations of PSU, and resampling approaches. The results suggest the PPS sampling design and it’s sampling weight can provided more precise parameter estimate of CFA models in a stratified sampling survey, no matter for continuous or categorical data. In resampling approaches, the accuracies and stabilities of JRR, Bootstrap and ABB are much better than RG.

第一章 緒論 1
第一節 研究動機 1
壹、重複取樣程序 4
貳、PSU異質性 6
參、取樣樣本數 7
肆、母群體資料型態 7
第二節 研究問題 8
第二章 文獻回顧與評述 9
第一節 取樣設計 9
壹、分層隨機取樣（Str. RS） 9
貳、等比率等機率取樣（PPS） 10
第二節 分層結構資料及SEM模式分析 10
第三節 Quasi Pseudo Maximum likelihood (QPML) 12
第四節 重複取樣程序及其權重計算 13
壹、Jackknife Repeated Replication (JRR) 13
貳、Bootstrap 16
參、Adjusted Balanced Bootstrap (ABB) 19
肆、Random Group (RG) 21
第三章 研究方法與進行步驟 25
第一節 模擬研究設計 25
第二節 取樣設計 27
壹、Jackknife Repeated Replication (JRR) 27
貳、Bootstrap 28
參、Adjusted Balanced Bootstrap (ABB) 28
肆、Random Group (RG) 29
第三節 結果分析 29
第四章 研究結果 31
第一節 連續資料 31
壹、取樣設計及不同重複取樣程序的影響 31
貳、取樣數（n）的影響 32
參、PSU異質性（d）的影響 34
第二節 類別資料 37
壹、取樣設計及不同重複取樣程序的影響 37
貳、取樣數（n）的影響 38
參、PSU異質性（d）的影響 40
第五章 結論與討論 43
第一節 取樣設計的影響 43
第二節 重複取樣程序的影響 44
第三節 取樣樣本數的影響 45
第四節 PSU異質性的影響 47
第五節 綜合討論 48
參考文獻 51
附錄 57
附錄一 連續資料下之參數估計及參數估計標準誤偏誤與MSE 57
附錄二 類別資料下之參數估計及參數估計標準誤偏誤與MSE表現 61
附錄三 PPS在連續資料之參數（ ）估計值分配 65
附錄四 Str. RS在連續資料之參數（ ）估計值分配 69
附錄五 PPS在連續資料之參數（ ）估計標準誤分配 73
附錄六 Str. RS在連續資料之參數（ ）估計標準誤分配 77
附錄七 PPS在類別資料之參數（ ）估計值分配 81
附錄八 Str. RS在類別資料之參數（ ）估計值分配 85
附錄九 PPS在類別資料之參數（ ）估計標準誤分配 89
附錄十 Str. RS在類別資料之參數（ ）估計標準誤分配 93

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