Young tableaux是在1900年代由Alfred Young提出。Young lattices的一些特性如ranked，存在最小元素，呈橄欖形，其完全配對的存在均已證出，對於配對問題的證明由於是用代數方法證出，其證明非常複雜因此我們希望能用離散的觀點加以探討。以期能發現簡易的證法。在本論文中將前人的一些結果加以整理，並以程式產生Young lattices觀察其特性。文中共提出二個演算法，一個用來產生Young lattices。另一個為產生Young Lattices配對的演算法。

中文摘要 中國大陸的金融業以引進外資是否可以改善盈餘管理是一個重要的研究議題，過去的文獻對此議題的研究結果並無一致性的看法。本文探討過去文獻上所使用的研究方法可能產生估計上的選擇偏誤，並提出以傾向分數配對方法(Propensity Score Matching Method)將樣本重新配對，以解決選擇偏誤的問題，並重新估計引入外資對改善盈餘的影響。首先，本文將所有資料分成兩組，試驗組(外資入股銀行)與控制組(外資沒入股銀行)並分別對其計算盈餘管理的統計量，發現不論是試驗組(外資入股銀行)或是控制組(外資沒入股銀行)均有盈餘管理現象，而控制組(外資沒入股銀行)的盈餘管理現象更較試驗組(外資入股銀行)嚴重的多，因此根據本文的實證結果本文初步的判斷外資入股會改善盈餘管理現象。然而，根據本文的實證研究，本文發現試驗組(外資入股銀行)與控制組(外資沒入股銀行)之後在樣本配對前，影響銀行從事盈餘管理行為的特性變數在兩樣本之間存在著顯著差異，而唯有透過配對方法篩選樣本後才減少了這個差異，而利用配對之後的樣本作分析，本文發現，平均來說，銀行引進外資的確會降低銀行從事盈餘管理的程度。

近年來，越來越多單身男女希望能夠透過網路交友平台找到自己的另一半。本論文考慮一個網路交友平台的經營，期望能夠讓每位參與者都找到適合彼此的另一半。我們使用工作指派問題的數學模型整合配對問題及穩定室友問題的概念建構男女配對問題的數學模型。並且考慮多位交友對象、拒絕對象與分級制度等問題，分別提出不同的數學模型。最後，我們使用隨機產生的資料模擬參與者的雙向配度，以GAMS軟體求解，分析不同的配對結果，亦探討不同模型的難易度及求解所需之運算時間。 / In recent years, more and more single women and men hope that they can find their Mr. or Mrs. Right through the internet dating platform. This paper considers the operation of an internet dating platform which expects each participant to find the other half of each other. We propose mathematical models of the women and men matching problem by using the mathematical model of the assignment problem and integrating the idea of matching problem as well as the stable roommate problem. We also consider the problems of multiple dating objects, matching with rejection, and classification member. Finally, a simulate study will be performed by using the randomly generating data to simulate the two-way matching degree of each pair of participants. We analyze the different matching results obtained by the different models. We also present the difficulty of different models and the solution times.

自民國71年來，癌症一直是台灣十大死因的首位。罹癌不但造成醫療費用的增加，也降低了病患的工作意願及能力。本文透過健保資料庫分析罹患肺癌及直腸、結腸癌對就業和薪資的影響。我們首先透過重大傷病檔選取公保和勞保人口中，新罹患肺癌和直腸、結腸癌病人為實驗組，再以配對估計法（prosperity score matching）從健保歸人檔中選取所對應的對照組；為了控制實驗組和對照組間難以觀察差異，本文進一步以「差異中之差異」（difference in difference），分析全職工作者（勞保、公保）罹患癌症對其就業及所得的影響。結果顯示癌症確對就業產生負面影響，在繼續存活的病患中，肺癌罹癌後兩年的平均就業率下降10.9％，大腸癌下降7.2％；其中女性的就業減幅約高於男性1.6~2.4倍，但公保和勞保的就業影響並無差異。在薪資上，罹癌後繼續就業者，與未罹癌者其薪資水準上並無顯著差異。

近年來，由於經濟體逐漸轉制和對外開放，中國大陸銀行業也逐漸接受全球化帶來的衝擊。然而外資進入對中國大陸銀行的績效究竟有無正向效果，各學者看法不一；在此議題上，過去的研究多限於法理推論或因中國大陸資料難以蒐集，並未能有完善的科學結果。本文即在探討中國大陸的城市銀行在外資參股後其績效是否優於其他城市銀行，綜合銀監會資料與Bankscope 資料庫，整理中國大陸111家城市銀行2004-2006年的財務資料，利用Rubin(1973)提出的配對理論(Matching Theory)檢驗外資是否能提升銀行競爭力。結果顯示外資參股的中國大陸城市銀行在淨利、不良貸款比率以及資本適足率三項指標上表現較佳，特定情況下外資參股的城市銀行在資產報酬率也有較佳的表現；但股東權益報酬率差異則不顯著。

過去十年，適婚年齡市場中的單身男女比率大幅成長，從1997年到2007年人口數共成長了10%，許多適婚未婚男女在茫茫人海中，希望運用不同的相親管道來找尋未來的伴侶。在所有選擇當中，婚友社是所有管道中最有效率的，透過婚友社媒合的平台，能快速拓展網絡效益，比較起網路交友、親朋好友介紹、其他不同型式的聯誼活動等等，如以找尋未來結婚伴侶為前提，婚友社是最好的選擇。 但是，最好的選擇並不等於最優先的選擇，許多人對於婚友社的印象，是比較負面的，認為它無法提供有品質的服務，能確實介紹適合自己的異性做為認識，甚至擔心付費後會員權益沒有保障，對婚友社運作流程沒有信心。市面上各式各樣規模的婚友社不少，但似乎還沒有一間夠穩定、可靠且擁有龐大的經濟規模，為整個產業的領導者，此篇研究，就是要建立起婚友社最重要的核心價值之一 - 標準化的配對機制，滿足顧客最根本的需求，創造差異化及提升競爭優勢，達到良好的口碑效益。 在研究中，與個案公司-中華民國佳緣婚友推廣協會配合，由資深紅娘蔡郁莉小姐做為公司代表，進行多次訪談，來了解公司整體運作狀況後，再深入探討既有配對流程和步驟。同時與佳緣會員及相關業者也安排了一對一訪談，了解整體產業內外部環境、競爭狀態和會員為滿足的需求等等，再透過外部資料，如:文獻探討、期刊、相關書籍等做彙整後，找出解決方案，制定出標準化的配對機制。 透過資料的彙整，最終找出兩性在找尋未來的伴侶，可從十個不同層面做擇偶條件設定，依照會員背景和需求的不同，也會影響到擇偶條件的設定。將這些條件設定的規則視為配對機制的主要因素，經過相互配對和條件篩選，進一步發展為標準化配對機制三大流程，能從龐大的會員資料庫中，有效率幫會員找出最合適的對象，成為在產業中首先建立客製化的配對機制的公司，提升配對效率及成功率，成為核心競爭價值之一，增加會員信賴度，和需求滿足，更重要的是，能將紅娘對會員了解的內隱知識外顯化，讓資訊不斷層，能完整的保留且傳承下去，維持一致的服務品質，創造佳緣專業的形象，扭轉外界原先對婚友社負面刻版印象，最終成為適婚未婚男女在尋找伴侶上，優先考量的管道之一，能招募更多新的會員。 美中不足的是，這套機制還未能實際在佳緣內部操作，無法了解實務上運作的效益及需改進之處，且也無法確定是否能套用在其他婚友社裡。在未來，除了要建立高效率的配對機制以外，還需要進一步探討如何來深耕與會員間的關係，提供其他未滿足的服務需求。 / Over the past decade, the rate of single man and woman in marriageable age in the market rise dramatically, it increased a total of 10% from 1997 to 2007. The unmarried man and woman searching different ways to meet new friends, and wishing they could become their future partner. In those different ways of meeting a possible future husband or wife, I would like to conclude that through organized one by one matchmaker platform would be the most efficient way. In this platform, people can expand their friend network quickly, compared to make friends online, introduced by relatives or close friends, or other different types of matchmaker activities. But if you want to find a future husband or wife, the one by one matchmaker organization will be the first and the best choice. However, the best choice does not necessary mean the most preferred choice, many people’s impression towards matchmaker organizations, is relatively negative, they think it is unable to provide good quality of service, cannot really introduce the specific right person for you to know, or some of them even worry that after they became a member, they will start to get less attentions. They simply have no faith in those matchmaker companies.They are all kinds of matchmaker companies, but none of them are known as the leader brand in this entire industry yet. This study, is to help this case company to develop it’s own differentiated advantage by establishing the most important core values system - standardize pairing mechanism. The purpose is to meet customers fundamental demands, which is help to find Mr or Ms Right for them quickly. It will also be able to achieve a good reputation for its effectiveness. In this study, the case company-Chiayuan , with the senior matchmaker representative, Ms. Tsai Yu-Lio were involved , provided many useful and valuable information. With several times of interviews, I have come to an understanding of how the company operates, and further more, to know their present process of pairing procedures.At the same time, I was arranged to have one by one interviews with the members of Chiayuan and also the people used to work for other matchmaker companies. From those interviews I get a closer look into the whole industry both internal and external environment situations, competitive status and member’s vital unsatisfied needs. Through the external data, such as: a literature discussion, periodicals, published books, etc., after I consolidated the information, I was able to work out the proper solutions to develop a standardized pairing mechanism.Through the data being deliberated, eventually I could find out the tracks on how the two sexes find their future partner. We can look at it from ten different required items, in accordance with the member’s different backgrounds and needs, can also affects how they set their requirements base on the those ten items and using those as the basic factors when processing the pairing mechanism. Through the filtering, we can develop three major steps for this pairing mechanism. The mechanism can help the matchmakers to identify the most appropriate member to match. There are no other companies has developed this kind of mechanism yet. This mechanism could enhance the matching process efficiency and improve the success rates, to become one of the core competitive value.It can increase the the dependability from members. More importantly, this mechanism can make the implicit knowledge into storable information, and stays in the company, maintaining consistent service quality, emphasize a professional brand image for Chiayuan. But this mechanism has not actually been used in Chiayuan as part of their internal procedure, therefore cannot be sure the practical benefits and necessary improvements. Addition to establishing the efficient pairing mechanism, we also need to explore further to know how to commit with the members, and provide them other unmet demand of services.

在勞動市場裡可以觀察到，每個人的工資都不相同。在過去的研究裡，學者嘗試以各種人力資本變數來解釋工資率的差異。其中，在男性的工資方程式中，婚姻狀態特別受到關注，且在過去研究皆發現男性存在著婚姻溢酬。文獻上解釋婚姻溢酬的來源，主要分成三個假說，分別是家庭分工假說、選擇性假說以及雇主的偏好。 本文和過去研究不同的地方在於消除選擇性偏誤的方法。我利用傾向分數配對法使婚姻狀態變成一個隨機決定的過程。配對完，並將資料整理為追蹤資料的型態後，再估計婚姻溢酬。最後結果顯示，在利用配對方法把單一年度資料轉換為兩期的追蹤資料後，婚姻溢酬仍然相當顯著，因此本文不支持選擇性假說。但是因為追蹤資料涵蓋期間過短，因此我無法利用現有的資料區分出家庭分工和雇主的偏好這兩種效果。 / The study of determinants of individual wages is important for exploring why some individuals earn more than other individuals. In the past, numerous efforts have been devoted to explain wage differentials by various human capital variables. Marital status is also used as a control and is of interest in estimating the male’s wage regression. It is commonly acknowledged that in cross-sectional analyses, married men have higher wages than single men, other things being equal. The higher wages paid to married men compared with their single counterparts is defined as marital wage premium. There are three leading hypotheses: family role specialization, selection hypothesis and employer favoritism. This paper uses a new method called propensity score matching to estimate the male marital wage premium. Propensity score matching is used to create a quasi-experiment that makes the decision to get married become a random treatment. The principle is to match a married man to a comparable single man who is closest in terms of important characteristics. And then, I transform the matched sample into panel data where units are observed at two periods, having the unmarried man as a proxy of married man, as if he was single. Therefore, I can apply fixed effect and random effect models to the transformed data. The results show no evidence to support the selection hypothesis since after transforming the data into panel data set and applying the fixed effect model, the marital wage premium is still significant. But being limited by the short period of the quasi-panel data set, I cannot distinguish between family role specialization and employer preference.

各式應用領域常會面臨許多撮合(Matching)問題，但當我們有需求時卻往往無法定出好的撮合策略，更遑論找到可實現此策略的電腦化解決方法。本研究希望針對穩定婚姻配對、大學聯考分發、論文審查分配、專題選修等等之類的撮合問題提供各種可行的通用撮合策略，可供使用者依其需求快速選用。而後續提供的支援系統則可據此產生一個以WEB為基礎的客製化專門應用領域撮合系統。 而什麼是撮合呢? 撮合是指有A、B兩群對象，在特定的規則與限制條件下，希望使每一A(B) 群對象可以連結至某些B(A)群對象，而使總體滿意度達到最大。以數學而言，一個A、B兩群間的撮合，就是一個滿足特定條件的A、B兩個集合間的二元關係。撮合類型可能是一對一、一對多、 多對多三種。一對一表示一個A群成員只能跟一個B群成員配對，一對多表示 一個A(B) 群成員能跟多個B(A) 群成員配對，多對多則指一個A群成員能跟多個B群成員配對且一個B群成員也能跟多個A群成員配對。 由於撮合型態與策略具有相當大的分歧性，以專用演算法實做並不實際，因此我們採用ASP(Answer set programming)實做撮合程式。ASP 是一種邏輯編程語言，具有宣告式程式特性，廣泛用於組合性問題的解決上，極適合應用在撮合策略的制定與實做。 在可真正執行撮合程式之前，必須預先建置A、B兩群對象的基本資料，因此我們的系統將允許開發者輸入A、B兩群對象的基本後設資料及撮合策略，而系統將據此建立對應Web介面與資料庫，允許使用者建立撮合對象的基本資料。一旦基本資料建立完成，系統即可依據系統設定的撮合策略以及以ASP實做的基本配對規則快速產生撮合結果，提供給使用者參考。 / There are a lot of application domains in which we may encounter the problem of finding a matching among two parties of entities. However, it is often the case that once a matching is needed, we cannot easily find a good matching strategy suitable for our purpose, not to mention one with a computerized implementation. This thesis aims to provide a web-based matching generation system allowing the quick generation of customized matching systems for users' need after their input of different demands of matching types and strategies. The supported types of matchings include most often used cases such as marriage/dating matching, paper review assignment, college admission dispatch and student-advisor selection etc. What is a matching? A (bipartite) matching problem contains two parties of entities, each member of which has a preference over members of the opposite party. A matching in a matching problem is a binary relation between both parties of entities. The goal of a matching problem is to find one or more optimal matching in which the total satisfaction of both party members is maximized. Matching problems can be classified according restrictions imposed on matchings. 1-1 matching requires each member of both parties to be matched to at most one opposite party member, 1-m matching allows only members of one party to be matched to more than one opposite party member, and m-m matching allows members of both parties to be matched to more than one opposite party member. Because there is a great variety of matching types and strategies, it is impractical to employ dedicated algorithm per case. It is thus eagerly expected to have a general framework in which different types of matching and strategies can be encoded. By applying Answer-set Programming (ASP) we provided one such framework in this thesis. ASP is logic programming language with declarative characteristics, widely applied in the solution of hard combinatorial problems, to be used in the encoding and solving of matching problems with different preference matching strategies. Theoretical discussion of matching algorithms always assumes that party members and their preferences are available in advance. However, to engineer a matching system, we still need to provide means to achieve it. Our system is thus also a matching support system, through the web interface of which developers and end-users can enter meta and individual information about all concerned properties and/or preferences of party members. After a possibly further processing of users' preference on the values of concerned properties of opposite party members for deriving every member's preference on the member of the opposite party, succeeding matching thus can obtain all needed data.

在觀察性研究或非隨機試驗研究中，欲探討因果效應時，研究者需要重新對觀察性研究進行設計，設計目的在於重新建立一個隨機指派受試者的機制，使其得以近似一個隨機試驗研究，這樣的研究一般稱為「類隨機試驗研究」(quasi-randomized-experiments)。 傾向分數分析即為一種設計觀察性研究的方法，在不牽涉到反應變數結果之下進行設計。本文於一個病例對照研究(case-control study)中使用傾向分數進行配對接著再進一步估計處理效果，傾向分數配對是可降低觀察性研究中的選擇性偏誤的方法，透過配對可減少實驗組與對照組間的系統性差異，使研究群體在所觀察到的控制變數分配達到相似，進而得到處理效果(treatment effect)的不偏估計，為近年廣受流行病學、經濟學以及社會學領域使用的方法之一。傾向分數本身為一個條件機率，定義為研究受試者在其所觀察到的控制變數之下，接受某處理或被指派至某特定群體的機率，估計傾向分數最常見的方法為羅吉斯迴歸。 此外，自1970年代起，配對方法(matching method)開始被使用來選取合適的實驗組與對照組並進行兩群體的比較，其中「確切配對」屬於最常使用的配對方法，過去文獻中經常可見各種配對方法的結合使用，因此，本文電腦模擬研究部份，欲比較四種情境之下「傾向分數配對」與「確切配對」結合使用的效果，分別以偏誤降低比例、信賴區間覆蓋率、均方誤衡量兩種配對方法結合使用的適合情境。結果顯示若對「與處理指派中度相關的變數」且「與反應變數高度相關的變數」，其效果最為明顯。根據結果，我們總結認為「確切配對與傾向分數配對合併使用」確實會有較好的表現，但表現的好壞也取決於確切配對的變數。實證研究部份，探討家庭結構對青少年偏差行為之影響，欲了解來自非完整家庭之青少年是否較來自完整家庭之青少年更有容易出現偏差行為。 / In observational or nonrandomized studies, treatments are not randomly assigned so that baseline differences between treated and control groups are typically observed. Without properly executed, the differences would bias the treatment effect estimates. There has been a long history of using matching to eliminate confounder bias, and inferences are made based on the matched observations. The theoretical basis for matching has been developed since 1970, and among those matching methods commonly in use, the exact matching is probably the most popular one. On the other hand, introduced by Rosenbuam and Rubin in 1983, propensity scores, the conditional probability of being exposed or treated given the observed covariates, has been a welcome alternative used to adjust for baseline differences between study groups of late. Instead of matching a treated with an untreated subject by their covariates, subjects in both treated and control groups are matched by their propensity scores. In this study, we explore the benefits of using propensity score matching together with the exact matching for adjusting for baseline differences through Monte Carlo simulations. An empirical study is also be provided for illustration.

在實務上，複選題分析一直處於觀察樣本情形的階段；至於進行檢定以推估母體情形的過程，則幾乎沒有人考慮到。就算曾經試圖想作類似檢定，卻也常常找不到可供參考的文獻或是使用了不適當的分析方法。 本研究的主要目的在於探討各式各樣離散型態相關資料的分析方法，其中亦包含許多複選題的分析方法。幾乎每個方法皆附上範例來說明程式撰寫及分析過程，希望對有此需求的人能有所幫助。 / Problems with multiple responses are usually analyzed by observing only the sample proportions. People don't bother to make any inferences based on the sample information mostly because they do not know how to do it. Even for those who do go beyond the stage of descriptive statistics might not work it out correctly. In the study, we review statistical methods for analyzing dependent proportions, including multiple responses. Almost every method is supplemented with an example which explains the way a related SAS program is written and the way the output is analyzed and explained. We hope that the results presented here will be helpful to those who are engaged in any analysis of multiple responses.