臺灣博碩士論文加值系統

在進行具有「敏感性問題」的問卷訪查時 ,常利用隨機作答方式來保護受訪者及降低其不誠實回答情況,而使得推估敏感性群體之比例上更為精確。 本文將對Greenberg et al.(1969)所提出的無關聯問題隨機作答模式來探討伴隨共變數缺失情況下,以確認概似估計法(Validation Likelihood Estimator,(簡稱VLE法))於邏輯斯迴歸參數估計的有效性比較,探討當共變數資料有缺失情況且缺失型態為隨機缺失(MAR)及完全隨機缺失(MCAR)時,利用確認概似估計法於不同選擇機率來進行邏輯斯迴歸參數估計。我們推導出確認概似估計法的大樣本性質並證明出在邏輯斯迴歸參數估計的結果中,其利用估計的選擇機率參數法及無母數法會比使用真正的選擇機率更具有效性。最後,將我們所提出的確認概似估計法用於分析台灣有線電視私接率的問題。

Randomized response technique (RRT) is commonly used to guaranty privacy and reduce the number of dishonest responses to sensitive questions in a survey research. The procedure yields a more accurate estimate of the proportion of the prevalent population. This article deals with logistic regression of data obtained from the unrelated question RRT (Greenberg et al. 1969) design when the covariate data are missing at random (MAR) or completely at random (MCAR). In particular, we compare the efficiency of the validation likelihood estimator using different estimates of the selection probabilities, which may be treated as nuisance parameters. Furthermore, we develop the large sample theory, and show that, they are more efficient than the estimator using the true selection probability. The proposed method is illustrated using data from a cable TV study in Taiwan.

1.緒論----------------------------------------------------1
2.文獻回顧------------------------------------------------4
2.1 缺失型態的介紹--------------------------------------4
2.2 估計方法介紹----------------------------------------6
2.3 邏輯斯迴歸下之隨機作答模式-------------------------11
3.方法介紹與參數估計-------------------------------------16
3.1 資料型態的介紹-------------------------------------16
3.2 完整資料分析法-------------------------------------17
3.3 確認概似估計法-------------------------------------17
3.4 選擇機率未知之確認概似估計法-----------------------19
3.4.1 選擇機率以無母數法估計之確認概似估計法-------19
3.4.2 選擇機率以參數法估計之確認概似估計法---------20
3.5 漸近分配理論---------------------------------------21
4.統計模擬-----------------------------------------------24
4.1 模擬方法的介紹-------------------------------------24
4.1.1 參數平均數之估計-----------------------------24
4.1.2 變異數估計-----------------------------------25
4.1.3 信賴區間與涵蓋率之估計-----------------------25
4.2 模擬結果的方析-------------------------------------26
5.實際案例分析-------------------------------------------41
6.結論與建議---------------------------------------------43
參考文獻-------------------------------------------------44
附錄-----------------------------------------------------48

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