處理缺失之資料，已經有一些插補方法，但這些插補方法在不同情況下是否確實有效，仍有待探討pd Van Buuren et al.(2006) 對兩種不相容性模型 (一條件分配函數為線性，另一條件分配函數分別為平方及對數)進行討論，該論文依據模擬結果，僅表示在此兩不相容性模型下的插補方法似乎仍有效。本文則不僅嘗試解釋此兩模型為何有效，且進一步探討是否所有的不相容性模型插補後能與母體參數值相似而達到有效插補，並檢定其模擬後之結果，本文發現其答案為否定。 / There are some available imputation methods to deal with missing data. However, whether imputation methods based on conditional distributions are effective is still questionable. Van Buuren et al.(2006) discuss two incompatible conditional distributions models (one conditional distribution has a linear relation, the other conditional distribution has a squared or a logarithmic relation). According to their simulation results, Van Buuren et al.(2006) conclude that imputation methods based on these two incompatible models are effective. In this thesis, we try to explain why the two imputation models are effective. In addition, we discuss whether all imputation methods based on incompatible models give estimated parameter values close to the true values. The simulation results of these methods are also tested statistically to answer this question. In conclusion, we find the answer is negative.

在抽樣調查的資料中，可能因為題意不清、關係到個人隱私，或是議題太過於敏感而導致受訪者「拒答」。透過存在拒答的樣本資料來做分析探討時，很可能會造成偏誤的研究結果，因此如何處理無反應的資料常常是一項研究結果是否可信的重要關鍵之一。常見的處理方式通常是設法對這些拒答資料進行插補。然而插補的好壞一直沒有一個判定準則，分析結果亦常因此受到質疑。 本研究將針對葛特曼量表的資料型態，利用「正確率」的概念，用不同的插補方式，包括社會科學研究常使用的簡易插補法，以及多重插補法與最鄰近插補法等方法，透過計算正確率來比較插補的好壞以及推論適用的時機。本研究以「台灣社會變遷基本調查」第四期第三次的調查資料中，有關性態度的題目做為例子，將其中符合葛特曼量表的資料視為「黃金標準」，並按照其中拒答部分的形態，從黃金標準中製造拒答資料。隨著拒答率的上升，每種拒答形態對應的個數將等量放大。 研究結果發現，簡易插補法的正確率可以透過公式推導求出。在這筆資料之下，不論何種簡易插補方法，其正確率都不超過32%，但隨著拒答型態與社會開放程度的不同，拒答率會有很大的變化。多重插補法之下的結果比簡易插補法略好一些，有接近33%的正確率，但從便利性來看使用簡易插補法就比多重插補法來的高。最鄰近插補法的正確率是相對比較高的，最高可以達到約47%，然而執行上比較花費時間，以及正確率有隨著拒答率的上升而下降的趨勢都是最鄰近插補法可能的問題。 / In a questionnaire survey、respondents may refuse to answer certain items since the questions themselves are unclear、sensitive、or relating to personal privacy. An analysis result using a data set containing refusal responses might be biased、how to deal with survey refusals have thus drawn much attention of late. One popular approach is through the use of imputation. However、lacking a criterion to evaluate its performances、there exist debates concerning the usefulness of this approach. In this study、we compare Simple imputation Method、Multiple Imputation Method、and Nearest Neighbor Method to deal with refusals in a set of survey items forming a Gittman scale in terms of imputation accuracy. Data are taken from the 2002 Taiwan Social Change Survey (TSCS)、and the items of interest are about sexual attitude. The parts of data that satisfy perfect Guttman scale are treat as 「Gold Standard」、and refusals are generated according to the original refusal pattern appear in the data. The result shows that the accuracy associated with Simple Imputation can actually be derived theoretically. No matter which version of Simple Imputation is applied、the accuracy is no more than 32%. Multiple Imputations performs slightly better than Simple Imputation、the accuracy is about 33%. However、it is less efficient in terms of computer time. Although Nearest Neighbor Method has the best performance the three、and its accuracy can reach as 47%、it requires much more computer time than the other two methods、and the accuracy would decrease as the refusal rate goes up.

由於時代的急速變遷，人們所面臨的問題日趨複雜。在有限的人力與財力限制之下， 欲對目標母體（TARGET POPULATION ），作一詳細的調查與研究通 常是不可能的， 因此如何藉由抽樣方法從母體中抽取具有代表性的樣本是重要的。在抽樣調查的過程 中我們常常發現樣本回收率沒有原來預期的高，若我們只用回收的樣本去做資料分析 ，常常使我們做成的結果是偏誤（BIASED）。本文的目的即在針對此一問題，做一深 入的研究探討。 抽樣調查中無觀測值（NONOBSERVATION）通常有三種情況發生： （１）未包括的範圍（NONCOVERAGE ），（２）未回收（TOTAL NONRESPONSE ）（３ ）回答不完全（ITEM NONRESPONSE）。吾人針對回答不完全。使用插補法（IMPUTATI O ）予以研究，即是對於缺失資料的項目依據種插補法給定一些值，使回收的資料具 完整性，以利資料的分析利用。 在日常生活中經常會遇到斤欲研究變數Y 與其另一輔助變數X 有某種線性關係存在。 例如農作物產量與種植面積、家庭收入與家庭支出、１９８０年全市人口總數與１９ ７０年全市人口總數等。為方便研究起見，首先假設一簡單的線性迴歸模式： y I ＝ β × I＋εI εI ∼ i.i.d.Ｎ（O.σ□） 在上式中，若（XI，yI） i＝1，2，……n 為一完整的資料集，即n 個隨機樣本（X I，yI ）皆無缺失值，則β與σ□的最小平方估計式可以很快求出，現在假設y 值有 部份缺失值，則必須想辨法把缺失的 值補齊，才能進一步研究β與σ□的性質，本 文即針對下列六種插補法。（a ）平均插補法（MO）、（b ）隨機插補法（RO）、（ C ）分層平均 插補法（MC）、（d ）分層隨機插補法（RC）、（e ）簡單迴歸插補法（RG）及（f ）隨機迴歸插補法（RRS，RRN），根據所建立的模式，運用各種不同的插補法將缺失 值予以補齊後，對模式結果作理論的探討，並對各種插補法作綜合分析比較。 最後利用其理論結果，配合１９８６年美國零售交易普查資料作實證研究，並分析其 實結果。

多數關於願付價格(WTP)之研究中，遺漏資料通常被視為完全隨機遺漏(MCAR)並刪除之。然而，研究中的某些重要變數若具有過高的遺漏比例時，則可能造成分析上的偏誤。 收入在許多條件評估(Contingent Valuation)調查中經常扮演著一個重要的角色，同時其也是受訪者最傾向於遺漏的變項之一。在這份研究中，我們將透過模擬的方式來評估多重插補法(Multiple Imputa- tion) 於插補願付價格調查中之遺漏收入之表現。我們考慮三種資料情況：刪除遺漏資料後所剩餘之完整資料、一次插補資料、以及多重插補資料，針對這三種情況，藉由三要素混合模型(Three-Component Mixture Model)所進行之分析來評估其優劣。模擬結果顯示，多重插補法之分析結果優於僅利用刪除遺漏資料所剩餘之完整資料進行分析之結果，並且隨著遺漏比例上升，其優劣更是明顯。我們也發現多重插補法之結果也比起一次插補來的更加可靠、穩定。因此如果資料遺漏機制非完全隨機遺漏之機制時，我們認為多重插補法是一個值得信任且表現不錯的處理方法。 此外，文中也透過「竹東及朴子地區心臟血管疾病長期追蹤研究」(Cardio Vascular Disease risk FACtor Two-township Study，簡稱CVDFACTS) 之資料來進行實證分析。文中示範一些評估遺漏機制的技巧，包括比較存活曲線以及邏輯斯迴歸。透過實證分析，我們發現插補前後的確造成模型分析及估計上的差異。 / Most often, studies focus on willingness to pay (WTP) simply ignore the missing values and treat them as if they were missing completely at random. It is well-known that such a practice might cause serious bias and lead to incorrect results. Income is one of the most influential variables in CV (contingent valuation) study and is also the variable that respondents most likely fail to respond. In the present study, we evaluate the performance of multiple imputation (MI) on missing income in the analysis of WTP through a series of simulation experiments. Several approaches such as complete-case analysis, single imputation, and MI are considered and com-pared. We show that performance with MI is always better than complete-case analy-sis, especially when the missing rate gets high. We also show that MI is more stable and reliable than single imputation. As an illustration, we use data from Cardio Vascular Disease risk FACtor Two-township Study (CVDFACTS). We demonstrate how to determine the missing mechanism through comparing the survival curves and a logistic regression model fitting. Based on the empirical study, we find that discarding cases with missing in-come can lead to something different from that with multiple imputation. If the dis-carded cases are not missing complete at random, the remaining samples will be biased. That can be a serious problem in CV research. To conclude, MI is a useful method to deal with missing value problems and it should be worthwhile to give it a try in CV studies.

隨著網路普及，人們越來越常在網路上購物並在線上評價商品，產生了非常大的口碑效應。不論對廠商或對消費者來說，線上商品評論都已經變得非常重要；消費者能藉由他人購買經驗判斷產品優劣，廠商能藉由消費者評價來提升產品品質，目前已有許多電子商務網站都有蒐集消費者購買產品後的意見回饋。 這些網站中有些提供消費者能對產品打一個總分並寫一段文字評論，然而每個消費者所評論的產品特徵通常各有不同，尤其是較晚購買的消費者更可能因為自己的意見已經有人提過而省略。將每個人提到的文字敘述量化為數字分數時，沒有寫到的特徵將會使量化後的資料存在許多遺漏值。 同時消費者也有可能提到一些不重要的特徵，若能找到消費者評論中，各個特徵影響消費者的多寡，廠商就能針對產品較重要的缺點改進。本研究將會著重探討消費者所提到的特徵對產品總分的影響，以及這些遺漏值填補後是否能接近消費者真實意見。 過去許多填補遺漏值的方法都是一次填補全部資料，並沒有考慮消費者會受到時間較早的評論影響。本研究設計一套多重插補的方法並透過模擬驗證，以之填補亞馬遜網站的Canon 系列 SX210、SX230、SX260等三個世代數位相機之消費者評論資料。研究結果指出此方法能夠準確估計各項特徵對產品總分的影響。 / Online user-generated product reviews have become a rich source of product quality information for both producers and customers. As a result, many E-commerce websites allow customers to rate products using scores, and some together with text comments. However, people usually comment only on the features they care about and might omit those have been mentioned by previous customers. Consequently, missing data occur when analyzing comments. In addition, customers may comment the features which influence neither their satisfaction nor sales volume. Thus, it is important to find the significant features so that manufacturers can improve the main defects. Our research focuses on modeling customer reviews and their influence on predicting overall ratings. We aim to understand whether, by filling up missing values, the critical features can be identified and the features rating authentically reflect customer opinion. Many previous studies fill whole the dataset, but not consider that customer reviews might be influenced by the foregoing reviews. We propose a method based on multiple imputation and fill the costumer reviews of Canon digital camera (SX210, SX230, SX260 generations) on Amazon. We design a simulation to verify the method’s effectiveness and the method get a great result on identifying the critical features.

吾人在抽樣調查訪問中, 經常會遇到資料缺失的情形。一般分析者常僅用有反應的部 分資料, 或使用各種不同的插補法先將資料補齊之后( 若資料分析者具有此統計專業 知識的話 )來進行分析, 因此可能造成使用相同的估計式(estimator) 卻獲得不一致 的結果。 在本文之中, 吾人討論: 當母體里的兩個變數, 具有簡單線性回歸之關系時, 其中一 個變數有缺失值, 并且資料的缺失是隨機散失的情形下, 今以七種不同之插補法( 平 均插補法(MO), 隨機插補法(RI), 分層平均插補法(MC), 分層隨機插補法(RC), 簡單 回歸插補法(RG), 隨機回歸插補法(RRS及RRN)) 將資料補齊后, 對於吾人所熟悉之一 些統計量( 例如:E(β ),E(β ),E(σ ),Var(β ),… 等),會有什么影響。同時也討 論了比較這些插補法之優劣的一些依據。最后我們利用其理論結果, 配合1986年美國 零售交易普查資料作實證分析, 并且以電腦來模擬資料缺失的情形, 使用插補法補齊 資料后予以分析研究, 比較其與理論結果之差異。 本文共分五部分, 其架構如下: 第一章 緒論, 說明研究動機與目的, 并回顧以往文獻在插補法之探討。 第二章 各種插補法及相關符號之簡介與定義。 第三章 各種插補方法之綜合比較。 第四章 實證分析。 第五章 緒論。

資料在企業資訊來源中扮演了極為重要的角色，特別是在現今知識與技術的世代裡。如果對於一個有意義且具有代表性資料庫中的遺漏值能夠正確的處理，那麼對於企業資訊而言，是一個大有可為的突破。 然而，有時我們或許會遇到一些不是那麼完善的資料庫，當資料庫中的資料有遺漏值時，從這樣資料庫中所獲得的結果，或許會是一些有偏差或容易令人誤解的結果。因此，本研究的目的在於插補遺漏值為資料庫加值，進而根據遺漏值類型建立插補模型。 如果遺漏值為連續型，用迴歸模型和倒傳遞類神經模型來進行插補；如果遺漏值為類別型，採用邏輯斯迴歸、倒傳遞類神經和決策樹進行插補分析。經由模擬的結果顯示，對於連續型的遺漏值，迴歸模型提供了最佳的插補估計；而類別型的遺漏值，C5.0決策樹是最佳的選擇。此外，對於資料庫中的稀少資料，當連續型的遺漏值，倒傳遞類神經模型提供了最佳的插補估計；而類別型的遺漏值，亦是C5.0決策樹是最佳的選擇。 / Data plays a vital role as source of information to the organization especially in the era of information and technology. A meaningful, qualitative and representative database if properly handled could mean a promising breakthrough to the organizations. However, from time to time, we may encounter a not so perfect database, that is we have the situation where the data in the database is missing. With the incomplete database, the results obtained from such database may provide biased or misleading solutions. Therefore, the purpose of this research is to place its emphasis on imputing missing data of the value-added database then builds the model in accordance to the type of data. If the missing data type is continuous, regression model and BPNN neural network is applied. If the missing data type is categorical, logistic regression, BPNN neural network and decision tree is chosen for the application. Our result has shown that for the continuous missing data, the regression model proved to deliver the best estimate. For the categorical missing data, C5.0 decision tree model is the chosen one. Besides, as regards the rare data missing in the database, our result has shown that for the continuous missing data, the BPNN neural network proved to deliver the best estimate. For the categorical missing data, C5.0 decision tree model is the chosen one.

本研究之目的旨在探討成就測驗中，學生的不完整作答反應是否能利用插補法，對不完整作答反應資料進行彌補。研究者藉由試題參數與受試者能力參數的分析討論，期望能獲得支持插補技術應用於成就測驗的結論。研究欲探討的問題有三：（一）利用統計插補法所估算之替代值與實際作答反應之間是否有差異存在；（二）受試者之部分答題反應組型在經過插補後，與完全作答反應組型之分析結果是否有差異存在；（三）能否將統計插補技術應用於成就測驗模式中。 本研究程序包含兩部分，一為模擬資料（N=1000，3000，5000，l0000；缺失比例為5%，10%，15%，30%，50%）的分析，模擬研究主要作為實證研究結果的驗證與推論；另一個則為實證資料的分析與討論。針對不完整作答反應，基於IRT的強假設前提，以及成就測驗作答反應的資料型態，研究者選擇熱卡插補法(HOt Deck imputation method)的統計插補技術，分別對於實證資料與模擬資料中之各類樣本數，與不同缺失比率下的作答反應作插補。另又以EM插補法作對照分析。 根據研究結果與討論，提出以下幾點歸納結論：（一）當缺失比例不大時，能符合原本的資料分佈假設，但隨著缺失比例愈高，高至30%以上時，已漸不符合原本假設；（二）當缺失比例愈高時，各項參數之估計標準差值幾乎是最大的；若忽略未作答反應之受試者的表現時，其分析所得的參數估計值亦並未是最佳的，反而是將所有受試者的作答反應進行插補估計後，所得的參數估計標準差值才是最小、最佳的；（三）本研究中，主要以熱卡法為插補方法，而EM插補法並不符合本研究資料之性質，故若採用此法進行插補，則所得的估計標準差會是最大的；（四）經過模擬研究與實證資料的分析後，證明熱卡法所推估的未作答反應，與直接刪除未作答反應或不處理未作答反應的確有差異存在，且經過插補所產生的替代值，對於受試者的能力表現能提供更穩定有效的解釋力。 關鍵詞：熱卡插補法、不完整作答反應、成就測驗 / This purpose of this study is to infer the feasibility if examinees' non response could be made up, by using imputation method in non response or missing value of achievement test. The research design contains two procedures: one is simulation research (setting sample sizes are 1000, 3000, 5000, and 10000; percents of non response are 5%, 10%, 15%, 30%, and 50%), and the other is pragmatic research. Hot deck imputation method is the main concern method in this research. To test if this method fits to achievement test, EM method is used for comparison with the Hot deck imputation method. The results are as follows: 1. The distribution of below 30% percent non response data after imputated is the same as the original data, but following the higher percents of non response, the distribution is not match what we expected. 2. Applying Hot Deck imputation method to the achievement test with different sample size and different percents of non response, the researcher found that following the higher percents of non response in any sample size, the higher standard deviation happened. Besides, ignoring or deleting these non responses is not a good way to deal with this test response pattern. Imputating an appropriate answer for the non response by Hot Deck imputation method, we could get the least standard deviation of the test and ability parameters estimation, and get largest test information for examinees. 3. We found the Hot Deck imputation method is suitable for the data pattern of achievement test than EM method. There are different outcomes between Hot deck imputation method and EM method. Hot Deck imputation method also has accuracy parameter estimation. 4. Based on above discussions, this study suggested that Hot deck imputation method could cope with non response in achievement test pretty well. Key Words: Hot Deck imputation method, Non response, Achievement test

有賴電腦的輔助，企業或組織內部所存放的資料量愈來愈多，加速資料量擴大的速度。但是大量的資料帶來的未必是大量的知識，即使擁有功能強大的資料庫系統，倘若不對資料作有意義的分析與推論，再大的資料庫也只是存放資料的空間。過去企業或組織只把資料庫當作查詢系統，並不知道可以藉由資料庫獲取有價值的資訊，而其中資料庫的內容完整與否更是重要。由於企業所擁有的資料庫未必健全，雖然擁有龐大資料庫，但是其中資訊未必足夠。我們認為利用資料庫加值方法：插補方法、抽樣方法、模型評估等步驟，以達到擴充資訊的目的，應該可以在不改變原始資料結構之下增加資料庫訊息。 本研究主要在比較不同階段的資料經過加值動作後，是否還能與原始資料結構一致。研究架構大致分成三個主要流程，包括迴歸模型、羅吉斯迴歸模型與決策樹C5.0。經過不同階段的資料加值後，我們所獲得的結論為在迴歸模型為主要流程之下，利用迴歸為主的插補方法可以使加值後的資料庫較貼近原始資料，若想進一步採用抽樣方法縮減資料量，系統抽樣所獲得的結果會比利用簡單隨機抽樣來的好。而在決策樹C5.0的主要流程下，以類神經演算法作為插補的主要方法，在提增資訊量的同時，也使插補後的資料更接近原始資料。關於羅吉斯迴歸模型，由於間斷型變數的類別比例差異過大，致使此流程無法達到有效結論。 經由實證分析可以瞭解不同的配模方式，表現較佳的資料庫加值技術也不盡相同，但是與未插補的資料庫相比較，利用資料庫加值技術的確可以增加資訊量，使加值後的虛擬資料庫更貼近原始資料結構。 / With the fast pace of advancement in computer technology, computers have the capacity to store huge amount of data. The abundance of the data, without its proper treatment, does not necessary mean having valuable information on hand. As such, a large database system can merely serve as ways of accessing and storing. Keeping this in mind, we would like to focus on the integrity of the database. We adapt the methods where the missing values are imputed and added while leaving the data structure unmodified. The interest of this paper is to find out when the data are post value added using three different imputation methods, namely regression analysis, logistic regression analysis and C5.0 decision tree, which of the methods could provide the most consistent and resemblance value-added database to the original one. The results this paper has obtained are as the followings. The regression method, after imputation of the added value, produced the closer database structure to the original one. And in the case of having large amount of data where the smaller size of data is desired, then the systematic sampling provides a better outcome than the simple random sampling. The C5.0 decision tree method provides similar result as with the regression method. Finally with respect to the logistic regression analysis, the ratio of each class in the discrete variables is out of proportion, thereby making it difficult to make a reasonable conclusion. After going through the above studies, we have found that although the results from three different methods give slight different outcomes, one thing stands out and that is using the technique of value-added database could actually improve the authentic of the original database.

本研究旨在了解家庭作業與學習成就的關係。為達研究目的，本研究以階層線性模式分析「國際數學與科學教育成就趨勢調查」2007年4年級學生資料；2007年8年級學生資料；以及2011年8年級學生資料，接著，本研究再以結構方程模式的長期追蹤交叉延宕模式，分析「臺灣教育長期追蹤資料庫」2001年、2003年及2005年追蹤樣本學生資料，本研究主要發現： 一、臺灣4年級學生的學生層次數學家庭作業時間對數學學習成就有顯著負向地影響效果；學生層次科學家庭作業時間對科學學習成就也有顯著負向地影響效果。 二、臺灣4年級學生的班級層次數學家庭作業頻率對數學學習成就沒有顯著地影響效果；班級層次科學家庭作業頻率對科學學習成就也沒有顯著地影響效果。 三、臺灣8年級學生的學生層次數學家庭作業時間對數學學習成就有顯著正向地影響效果；學生層次科學家庭作業時間對科學學習成就也有顯著正向地影響效果。 四、臺灣8年級學生的班級層次數學家庭作業頻率對數學學習成就有顯著正向地影響效果；班級層次科學家庭作業頻率對科學學習成就也有顯著正向地影響效果。 五、臺灣2001年7年級陸續追蹤至2005年11年級的學生，其家庭作業時間與學習成就有顯著正向地相互影響效果。 / This study aimed analyze the relationship between homework and learning achievements. Hierarchical linear modeling was used to analyze the 4th grade of elementary school students from Trends in International Mathematics and Science Study (TIMSS) 2007, 8th grade of junior high school students from TIMSS 2007, and 8th grade of junior high school students from TIMSS 2011. Moreover, structural equation modeling with cross-lagged panel modeling was used to analyze the core panel sample data from Taiwan Education Panel Survey (TEPS) in 2001, 2003, and 2005. The major findings were as follows: 1. Taiwan 4th grade of elementary school students’ student-level mathematic homework time could negative predict the mathematic learning achievements significantly, and student-level science homework time could also negative predict the science learning achievements significantly. 2. Taiwan 4th grade of elementary school students’ class-level mathematic homework frequency could not predict the mathematic learning achievements significantly, and class-level science homework frequency could also not predict the science learning achievements significantly. 3. Taiwan 8th grade of junior high school students’ student-level mathematic homework time could positive predict the mathematic learning achievements significantly, and student-level science homework time could also positive predict the science learning achievements significantly. 4. Taiwan 8th grade of junior high school students’ class-level mathematic homework frequency could positive predict the mathematic learning achievements significantly, and class-level science homework frequency could also positive predict the science learning achievements significantly. 5. Taiwan 7th grade of junior high school students to 11th grade of senior high school students’ homework time could positive predict the subsequent learning achievements significantly, and learning achievements could also positive predict the subsequent homework time significantly.