在處理一般的線性模式的問題上，通常假設e 服從常態分配N （O ，σ□I ），其中 變異數σ□未知常數。因此我們利用最小平方法（LEAST SQUARE METHOD ）處理此類 問題前，必須先檢查誤差項是否滿足下列的假設： （１）每一誤差項均服從Ｎ（O ，σ□）。 （２）σ□為未知常數。 （３）誤差項間相互獨立（MUTUALL INDEPENDENT ）。 由於第（３）項的假設乃一般線性模式所需滿足的條件，因此若吾人之研究在線性模 式的範圍內時，一般均視此條件成立。至於第（１）項及第（２）項的檢驗方法，分 述如下： （一）檢驗常態性假設 統計上，多採用畫圖的方法來檢驗一樣本是否可視為常態，其中常用的方法為常態機 率圖（NORMAL PROBILITY PLOT ），當所畫出的圖形越接近一直線時，表示此樣本越 接近於常能分配。 （二）檢驗σ□是否常數 統計上使用最廣泛的檢驗法為BARTLETT'S TEST 檢定法，當誤差項獨立地服從常態分 配時，此法之檢定統計量（TEST STATISTIC）會接近於卡方分配（CHI-SQUARE DISTR IBUTION ），其自由度為n-1 。若統計量值太大，則拒絕虛無假設。 當第（１）項及第（２）項的假設無法滿足時，可用BOX-COX TRANSFORMATION的轉換 方法，找尋一適當轉換母數ν，一般均可接近上面假設的要求。 雖然運用最小平方法，在溝足誤差項獨立地服從N（O，σ□）的假設前項題下所求得 之參數（PARAMETER ）估計量，可得到一些良好的統計性質 ，如b.l.u.e ，但是我們將隨機誤差項的配局限於常態分配不盡合理，此外均方誤（ SUM OF SQUARE ERROR ）易受極端值的影響。因此令一解決方法，即是以無母數統計 方法來處理此問題。本文之目的主要是欲利用JAECKEL 所建的殘差離勢，發展出在線 性模式中大樣本的無母數檢定方法，因其方法類似於最小平方法的精神，其所得結果 與解釋方法，亦與最小平方法類似。 綜上所述，本文的研究範圍，乃在考慮一線性模式其誤差項獨立地服從一連績分配， 基於JAECKEL 建議的殘差離勢方法，發展出一般之無母數檢定方法。吾人將導出在虛 無假設成立下，其檢定統計量會趨近何種分配？為使此檢定之運用更廣，要求一母體 分配（UNDERLYING DISTRIBUTION ）之函數的一致估計式，令其（７）τ（Ｆ），吾 人亦將導出τ（Ｆ）的一致估計式。此外亦將探討其Ａ．Ｒ．Ｅ．（ASYMPTOTIC REL ATIVE EFFICIENCY）。 本文共分四章，第一章說明研究動機、目的、範圍及本文之大綱。第二章為迴歸係數 的估計及其近似分配；第一節為JURECKORA 的迴歸係數估計式；第二節為JACEKEL 的 迴歸係數估計式。第三章為線性等級統計量，在線性模式上的理論基礎，第一節為檢 定統計量及其近似分配；第二節為r 的一致估計式；第三節為近似相對有效性。第四 章為結論。

本文主要在探討評審間意見一致程度的問題, 除了回顧kappa係數和weighted kappa係數及其應用外. 並討論如何採用對數線性模型中加入代表一致程度的參數來分析這類的問題. kappa係數提供應用者一個快速獲得評審間意見一致程度的指標, 而利用對數線性模型分析, 則可以獲得更多的訊息. 因此, 我們嘗試將kappa係數和對數線性模型作一對比. 此外,針對三個評審間意見一致程度的問題我們也引進K-ABC係數, 並與模型log(m-ijk) = u + l(A, i) + l(B, j) +l(C, k) + Delta*I(i=j=k) 作以對比, 利用模擬實驗將Delta(hat)與K(ABC)所對應的可能範圍列出, 供使用者參考. / The focus of this study is on the measurement of interater agreement. Analyses in terms of kappa tyoe coefficients and in terms of loglinearmodel techniques are reviewed, and issues related to the two approaches adderssed. In additition, a new kappa type corfficient Kappa-ABC is introduceto provide indication of agreement among three raters. Its possible connections with the coefficient Delta in the model log(m-ijk) = u + l(A, i) + l(B, j) + j(C, k) + Delta*I (i=j=k) are studied.

傳統的犯罪學在於研究犯罪者生理與心理的特性以及外在環境因素，藉以 尋求預防犯罪的策略。其實，預防犯罪的目的是要減少被害者數目。因此 ，吾人希望藉由探討被害者家庭形態的特質與社會犯罪的關係，使防範被 害的政策能夠落實到家庭層面。所以本研究的目的就是要利用統計方法， 透過數字及圖形上的表達，來描述住戶之家計負責人的特性(如性別、年 齡、教育程度)與住戶遭受侵害的事實(曾或否)及類型(如財物侵害、暴力 侵害、其他侵害)之間的關係，期為犯罪統計工作提供一些分析的工具。 在本篇論文，首先利用對數線性模式分析，選出最適合的模式，以解釋家 計負責人之性別、年齡、教育程度與住戶是否遭受侵害等四個變數之間的 關聯性。接著利用推理值模式分析探討家計負責人之性別，年齡，教育程 度這三個解釋變數各分級對住戶遭受侵害之影響的主效應及交互作用效應 。最後則是利用對應分析處理資料，透過對應分析的顯示圖形，可以用來 解釋家計負責人之性別、年齡、教育程度以及住戶遭受侵害的犯罪類型之 間的對應關係。

本研究旨在探討猝睡症患者生活品質受症狀變化及神經認知功能改變的影響情況，以及不同層次影響因素對患者生活品質的初始狀態及後續變化軌跡的影響效果。 本研究於北部一所醫學中心睡眠障礙科及兒童心智科募集確診為猝睡症之患者，經同意後進行為期五年的長期研究，募集總人數168人，完成五年資料收集人數85人。本研究使用睡眠多項檢驗（polysomnography, PSG）、多段入睡測試（multiple sleep latency test, MSLT）、人類白血球抗原檢驗（human leukocyte antigen, HLA）為基本檢驗工具，以電腦化第二版康氏持續注意力測驗（Continuous Performance Test- II）及威斯康辛卡片分類測驗（Wisconsin Card Sorting Test, WCST）為檢測神經認知功能之工具，以自填艾普渥斯嗜睡程度量表（Epworth sleepiness scale, ESS）、史丹佛睡眠問卷（Stanford sleep inventory, SSI）及簡式生活品質量表（short from-36 items of health related quality of life, SF-36）做為症狀嚴重度及生活品質的依據。資料分析以描述統計及階層線性模式（hierarchical linear models , HLM）統計方法進行。主要結果如下： 一、 猝睡症患者生活品質分為生理與心理兩個層面，患者生理層面在五年期間維持相對穩定沒有顯著變化；心理層面中之不同向度則有不同變化趨勢，心理健康與活力向度隨時間有逐漸提高的趨勢，患者此二向度生活品質接受治療後有穩定上升的趨勢，而社會功能及情緒角色限制則呈現二次方曲線變化，以及呈現先增後減的發展軌跡，患者此二向度接受治療後顯著上升，第三年後有逐年下降的趨勢。 二、 患者嗜睡程度及猝倒嚴重度變化隨時間有顯著成長軌跡，呈二次方曲線發展，轉折點在第三年，接受治療前三年症狀呈現穩定降低的軌跡，但自第三年起逐年增加，此結果與藥物治療初期症狀獲得顯著改善，後期改善幅度相對減少，及藥物效果具有關聯。 三、 個體間層次變項僅疾病持續時間、HLA對患者生活品質具顯著解釋力，其中疾病持續時間越長，患者可能發展因應症狀之策略，從而降低疾病對生活品質之衝擊。而HLA則對症狀有不同影響，HLA陽性患者初始嗜睡程度較陰性者為低，且接受治療後改善效果較陰性者顯著，猝倒嚴重度起始值較陰性者高，且接受治療後的趕善幅度較陰性者小。 四、 疾病嚴重度變化對生活品質具顯著影響，完整模式分析中，時間主效應未達顯著，但可由症狀變化及神經認知功能改變進行更佳的解釋。嗜睡程度變化僅對身體疼痛向度變化不具有解釋力外，對其餘七個向度均具顯著影響；猝倒影響層面不及嗜睡程度，但亦可解釋生理量表、生理角色限制、心理量表、心理健康、情緒角色限制、活力等向度上的變化。 五、 神經認知功能改變與否對患者生活品質具有加成效果，分析顯示患者神經認知功能改善時，其生活品質提升速率較未改善者高，影響較顯著的包括注意力、警覺度及概念反應，此結果與下視丘泌素參與的維持注意力及前額葉功能有關。 本研究依據分析結果提出猝睡症患者生活品質受嗜睡症狀及猝倒嚴重度改變直接影響，同時受人類白血球抗原屬性及神經認知功能改變調節之假設模型，作為未來研究參考依據。並根據研究結果與限制，提出對臨床實務的應用與心理介入的建議，並對未來提升猝睡症患者生活品質相關研究提供建議。 / The current study aims to: (1) examine the change of eight domains of quality of life in narcoleptics within five years, (2) investigate the impact of the change of symptom severity on different dimension of quality of life, as well as the influence associated with the change of neuro-cognitive function. There were 168 participants recruited from a medical center in northern Taiwan. 85 of them completed the 5-year annual follow-up data collection. During the follow-ups, polysomnography (PSG), multiple sleep latency test (MSLT) and human leukocyte antigen (HLA) test were conducted. Computerized neuropsychological tests of Conners’ Continuous Performance Test- II (CPT-II) and Wisconsin Card Sorting Test (WCST) were also administered to obtain attention and executive function data. The short from-36 items of health related quality of life (SF-36), Stanford sleep inventory (SSI) and Epworth sleepiness scale were applied to assess quality of life and symptom severity. Descriptive statistics and hierarchical linear models were applied for data analysis. The main results were: 1. The quality of life was divided into physical and psychological domains. The physical domain kept relatively stable during the 5-year follow up as opposed to the psychological domain. In psychological domain, the vitality and psychological health showed increasing tendency overtime. However, the social function and role functioning-emotion increased during the first 3 years then declined afterward. 2. The symptom severity also showed a tendency corresponded to quadratic curve. The daytime sleepiness together with cataplexy severity reduced immediately after treatment but rose after the third year. 3. The variables of individual characteristics that showed significant impact on quality of life were disease duration and HLA type. The longer the duration, the better quality of life one had. Positive HLA typing seemed to be a protective factor on severity of sleepiness. It also predicted better treatment outcomes, but worsen the severity of cataplexy and treatment effects. 4. The symptom severity could be a good explanation as a variable of quality of life. The daytime sleepiness altered all domain of SF-36 expect body pain. Cataplexy affected only psychological domain of SF-36. 5. The neuro-cognitive function was also found to affect quality of life. Those who improved in attention and executive function test got greater improvement on SF-36 as well. The vigilance on CPT-II and conceptualized response on WCST had most significant impact. I proposed a model of change of quality of life in patients with narcolepsy based on the results obtained. Several suggestions were also proposed for clinical and psychological intervention for narcolepsy to improve their quality of life.

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本研究旨在建立廣義線性模式下之D-與A-最適設計(optimal designs)，並依不同處理結構(treatment structure)分成完全隨機設計(completely randomized design, CRD)與隨機集區設計(randomized block design, RBD)兩部分探討。 根據完全隨機設計所推導出之行列式的性質與理論結果，我們首先提出一個能快速大幅限縮尋找D-最適正合(exact)設計範圍的演算法。解析解的部分，則從將v個處理的變異數分為兩類出發，建立其D-最適近似(approximate)設計，並由此發現 (1) 各水準對應之樣本最適配置的上下界並非與水準間不同變異有關，而是與有多少處理之變異相同有關；(2) 即使是變異很大的處理，也必須分配觀察值，始能極大化行列式值。此意味著當v較大時，均分應不失為一有效率(efficient)的設計。至於正合設計，我們僅能得出某一處理特別大或特別小時的D-最適設計，並舉例說明求不出一般解的原因。 除此之外，我們亦求出當三個處理的變異數皆不同時之D-最適近似設計，以及v個處理皆不同時之A-最適近似設計。 至於最適隨機集區設計的建立，我們的重點放在v=2及v=3的情形，並假設集區樣本數(block size)為給定。當v=2時，各集區對應之行列式值不受其他集區的影響，故僅需依照完全隨機設計之所得，將各集區之行列式值分別最佳化，即可得出D-與A-最適設計。值得一提的是，若進一步假設各集區中兩處理變異的比例(>1)皆相同，且集區大小皆相同，則將各處理的「近似設計下最適總和」取最接近的整數，再均分給各集區，其結果未必為最適設計。當v=3時，即使只有2個集區，行列式也十分複雜，我們目前僅能證明當集區內各處理的變異相同時(不同集區之處理變異可不同)，均分給定之集區樣本數為D-最適設計。當集區內各處理的變異不全相同時，我們僅能先以2個集區為例，類比完全隨機設計的性質，舉例猜想當兩集區中處理之變異大小順序相同時，各處理最適樣本配置的多寡亦與變異大小呈反比。由於本研究對處理與集區兩者之效應假設為可加，因此可合理假設集區中處理之變異大小順序相同。 / The problem of finding D- and A-optimal designs for the zero- and one-way elimination of heterogeneity under generalized linear models is considered. Since GLM designs rely on the values of parameters to be estimated, our strategy is to employ the locally optimal designs. For the zero-way elimination model, a theorem-based algorithm is proposed to search for the D-optimal exact designs. A formula for the construction of D-optimal approximate design when values of unknown parameters are split into two, with respective sizes m and v-m, are derived. Analytic solutions provided to the exact counterpart, however, are restricted to the cases when m=1 and m=v-1. An example is given to explain the problem involved. On the other hand, the upper bound and lower bound of the optimal number of replicates per treatment are proved dependent on m, rather than the unknown parameters. These bounds imply that designs having as equal number of replications for each treatment as possible are efficient in D-optimality. In addition, a D-optimal approximate design when values of unknown parameters are divided into three groups is also obtained. A closed-form expression for an A-optimal approximate design for comparing arbitrary v treatments is given. For the one-way elimination model, our focus is on studying the D-optimal designs for v=2 and v=3 with each block size given. The D- and A-optimality for v=2 can be achieved by assigning units proportional to square root of the ratio of two variances, which is larger than 1, to the treatment with smaller variance in each block separately. For v=3, the structure of determinant is much more complicated even for two blocks, and we can only show that, when treatment variances are the same within a block, design having equal number of replicates as possible in each block is a D-optimal block design. Some numerical evidences conjecture that a design satisfying the condition that the number of replicates are inversely proportional to the treatment variances per block is better in terms of D-optimality, as long as the ordering of treatment variances are the same across blocks, which is reasonable for an additive model as we assume.

本論文從教育社會學角度探討造成數學成就性別差異現象的成因，以班級的性別環境為研究脈絡，研究影響國中女生數學成就的可能原因。假設數學成就的性別差異是受到後天學習歷程影響，班級環境中隱含的性別刻板印象為其中一個重要社會文化影響因素。透過比較國一到國三階段女生班和一般男女合班女生數學成就的異同，嘗試找出造成數學成就性別差異現象的成因，是否與班級性別環境、師生的性別刻板印象等因素有關。利用階層線性模式（Hierarchical Linear Models，HLM）統計方法，分析資料取自由中央研究院、教育部和國科會共同規劃的全國性長期的調查計畫：「台灣教育長期追蹤資料庫」（Taiwan Education Panel Survey，簡稱TEPS）。研究結果發現女生班、數學老師性別及班級學業氣氛等因素對於國中女生數學成就有顯著影響力，但進一步考慮學校公私別變項之後，女生班的影響力即消失。 / The main purpose of this study is to assess the magnitude of individual and contextual influences to explain gender differences in math achievements. Adopting the hierarchical linear model analysis to determine whether or not statistically significant differences between the mathematical achievements of 7th grade students who attend all-girls classes compared with those who attend coeducational classes at the same time, and their academic performance after two years. The result shows that there are three factors that have significant influences on girls’ math achievement in junior high schools, which are the single-sex classes, female math teachers and the academic climate of each class. However, if private schools are taken into consideration, the significant influence of the gender composition of classes will disappear.

本研究以TIMSS 2003台灣數學科資料為資料來源，使用階層線性模式為統計分析方式，探討國小四年級及國中二年級，學生數學家庭作業完成時間與教師指派數學家庭作業頻率，對於學生數學學習成就的影響。研究結果顯示：在國小四年級，學生數學家庭作業完成時間與學生數學學習成就為負相關；教師指派數學家庭作業頻率與學生數學學習成就之間為正相關，但並不顯著。在國中二年級，學生數學家庭作業完成時間與教師指派數學家庭作業頻率，對學生數學學習成就皆有正向的影響。在國小四年級中，學生數學家庭作業完成時間與教師指派數學家庭作業頻率的交互作用，對學生數學學習成就為負相關，但不顯著。在國中二年級中，學生數學家庭作業完成時間與教師指派數學家庭作業頻率的交互作用，對學生數學學習成就為正相關，但不顯著。 / The research was to explore the effects of mathematics homework time and mathematics homework frequency on mathematics achievement in the fourth and eighth grades, using TIMSS 2003 Taiwan mathematics data as the resources and Hierarchical Linear Modeling as the statistical analysis method. The results showed that in the fourth grades, mathematics homework time had a negative relationship with mathematics achievement while mathematics homework frequency had a positive, but non-significant, relationship with mathematics achievement. In the eighth grades, both mathematics homework time and mathematics homework frequency had positive effects on mathematics achievement. In the fourth grades, the interaction between mathematics homework time and mathematics homework frequency had negative, but non-significant, effects on mathematics achievement while in the eighth grades, the interaction between mathematics homework time and mathematics homework frequency had positive, but non-significant, effects on mathematics achievement.

近來，臺灣教育部為招收更多國際學生而實行新政策。本研究分析政策實行的效果、學生來臺原因及在臺學生的滿意度。研究一以時間序列分析1954至2008年的國際學生人數，ARIMA模式的預測效果良好(RER=0.83%)，未來三年內國際學生人數將突破二萬人。研究二以問卷調查分析學生選擇留學國家及學校的選擇因素，同時分析學生來臺動機、所遇困難及在臺滿意度間的關係 (N=210)。結果顯示容易的簽證程序及臺灣的學術聲望影響學生來臺讀書；此外，財務、後勤及生活條件影響學生選擇留學學校。學生因臺學術聲望來臺且無食物適應困難者，願意再次來臺念書；學生因具吸引力課程及方便生活環境來臺且無硬體設備及學習適應方面困難者，願意建議他人來臺留學。根據研究結果，政府應加強國內教學品質，並協助提升學校學術聲望；增加赴海外任教教師，以教學專業提升我國國際形象。有興趣吸引國際學生的學校應可從健全學校行政體制著手，並聚焦於完善學生招生、入學諮詢輔導工作及協助生活適應。 / Recently, the Taiwanese Ministry of Education has implemented a new policy to recruit more international students. This study analyzes the policy’s effects and the reasons motivating students to study in Taiwan. The number of international students in Taiwan from 1954 to 2008 was used to generate a time series model to estimate the number of international students before and after the policy implementation. This ARIMA model (RER=0.83%) demonstrated a dramatic increase in the number of international students over the years. Using a questionnaire designed to examine determinants that affect international students’ decisions for choosing Taiwan and their respective schools (N=210), this study then study the relationship between the students’ motivations, the challenges they faced, and their degree of satisfaction with their experiences. Results demonstrated that an easy visa application process and Taiwan’s acclaimed academic reputation attracted students. Furthermore, financial, logistical, and living reasons affected the students’ choices in schools. Students who found living and educational conditions favorable and who felt intellectually stimulated would choose again to study in Taiwan and would recommend others to do so. Based on these results, the government should strengthen the quality of instruction and further promote Taiwan’s universities abroad. Schools interested in attracting international students should develop structured administrative systems focused on recruiting students and helping them transition into a new environment.

20世紀以來，因為衛生醫療等因素的進步，各年齡死亡率均大幅下降，使得平均壽命大幅延長。壽命延長的效果近年逐漸顯現，其中的人口老化及其相關議題較受重視，因為人口老化已徹底改變國人的生活規劃，死亡率是否會繼續下降遂成為熱門的研究課題。描述死亡率變化的模型很多，近代發展的Age–Period–Cohort模型(簡稱APC模型)，同時考慮年齡、年代與世代三個解釋變數，是近年廣受青睞的模型之一。這個模型將死亡率分成年齡、年代與世代三個效應，常用於流行病學領域，探討疾病、死亡率是否與年齡、年代、世代三者有關，但一般僅作為資料的大致描述，本研究將評估APC模型分析死亡率的可能性。 APC模型最大的問題在於不可甄別(Non–identification)，即年齡、年代與世代三個變數存有共線性的問題，眾多的估計APC模型參數方法因應甄別問題而生。本研究預計比較七種較常見的APC模型估計方法，包括本質估計量(IE)、限制的廣義線性模型(cglim_age、cglim_period與cglim_cohort)、序列法ACP、序列法APC與自我迴歸模型(AR)，以確定哪一種估計方法較為穩定，評估包括電腦模擬與實證分析兩部份。 電腦模擬部份比較各估計方法，衡量何者有較小的年齡別死亡率及APC參數的估計誤差；實證分析則考慮交叉分析，尋找用於死亡率預測的最佳估計方法。另外，也將以蒙地卡羅檢驗APC的模型假設，以確定這個模型的可行性。初步研究發現，以台灣死亡資料做為實證，本研究考量的估計方法在估計年齡別死亡率大致相當，只是在年齡–年代–世代這三者有不同的詮釋，且模型假設並非很符合。交叉分析上，Lee–Cater模型及其延展模型相對於APC模型有較小的預測誤差，整體顯示Lee–Cater 模型較佳。 / Since the beginning of the 20th century, the human beings have been experiencing longer life expectancy and lower mortality rates, which can attributed to constant improvements of factors such as medical technology, economics, and environment. The prolonging life expectancy has dramatically changed the life planning and life style after the retirement. The change would be even more severe if the mortality rates have larger reduction, and thus the study of mortality become popular in recent years. Many methods were proposed to describe the change of mortality rates. Among all methods, the Age-Period-Cohort model (APC) is a popular method used in epidemiology to discuss the relation between diseases, mortality rate, age, period and cohort. Non-identification (i.e. collinearity) is a serious problem for APC model, and many methods used in the procedure included estimation of parameter. In the first part of this paper, we use simulation compare and evaluate popular estimation methods of APC model, such as Intrinsic Estimator (IE), constrained of age, period and cohort in the Generalized Linear Model (c–glim), sequential method, and Auto-regression (AR) Model. The simulation methods considered include Monte-Carlo and cross validation. In addition, the morality data in Taiwan (Data sources: Ministry of Interior), are used to demonstrate the validity and model assumption of these methods. In the second part of this paper, we also apply similar research method to the Lee-Carter model and compare it to the APC model. We found Lee–Carter model have smaller prediction errors than APC models in the cross–validation.