本研究的目的在於結合部份計分模式(partial credit model, PCM)與模糊集合論(fuzzy set theory)，提出評定量表的不同計分方式：模糊部份計分法(fuzzy partial credit scaling, FPCS)。FPCS是根據 PCM 所估計出的梯度參數(step parameters)來建構三角形模糊數，三角形模糊數代表選擇某個特定選項的受試者的能力分配情形。接著，利用中心法(center of gravity method) 將三角形模糊數解模糊化為純量。最後，利用隸屬度當作權重，計算個別受試者的模糊觀察分數，並且用模糊觀察分數當作量表的總分。 本研究採用貝克憂鬱量表(Beck Depression Inventory-II, BDI)中文版為研究工具。本研究的樣本分為憂鬱症病患與非憂鬱症的一般大學生兩大類。240位憂鬱症病患樣本是由台北市立和平醫院精神科門診募集而來；321位大學生則以便利抽樣的方式募集而來。 為了驗証FPCS的有效性，本研究進行三個子研究，來比較FPCS與傳統計分法在信度、效度、集群分析的分類正確性。 子研究一探討FPCS的信度。本研究以Cronbach alpha係數來衡量量表的內部一致性，並且以結構方程式模式(structure equation modeling)進行驗證性因素分析所估計的各試題的變異數被潛在構念解釋的比例當作信度的指標。由研究結果顯示，以量表整體而言，FPCS計分的結果得到較高的內部一致性；以各題而言，量表各試題的變異數被潛在構念解釋的百分比高於傳統的原始分數。此結果顯示FPCS的計分方式可以降低測量誤差，提升信度。 子研究二探討FPCS的效度，本研究以精神科醫師的診斷當作效標，分別以FPCS與原始分數兩種不同的計分法當作自變項，以預測效度當作效度的指標。首先，將是否罹患憂鬱症編碼為二元變數，不同計分法所得到的量表分數當作自變數，進行Logistic迴歸分析。研究結果顯示，相較於原始分數，FPCS預測罹患憂鬱症的正確率由 74.8% 提升到 77.2%。接下來，依照所有樣本的憂鬱程度，區分為一般樣本、憂鬱症且緩解、憂鬱症無緩解三類，進行區別分析。研究結果顯示，相較於原始分數，FPCS分類正確率由 71.2% 提升到 80.7%。上述的研究結果顯示，FPCS具有較高的效度，可以降低誤判憂鬱症的機率。 子研究三比較模糊集群分析(fuzzy c-means, FCM)與傳統明確邏輯的集群分析。首先利用分群效度(clustering validity)指標，決定群數為三群。並以此結果，指定模糊集群、Wald法、k-means法之群數。為了比較分類的效果，將模糊集群之樣本，指定給獲得最大隸屬度之集群。並且以醫師的診斷的憂鬱程度當作評估分類結果之標準。研究結果顯示，相較於傳統明確邏輯的集群分析(Wald法、k-means法)，模糊集群分析得到分群結果，與醫師的診斷的結果有最高的相關。結果顯示模糊集群分析更能夠忠實的反映資料結構。 整體而言，相較於原始分數，FPCS有較高的信度、效度、分類正確性。此實証性研究結果支持了模糊集合論應用於心理學研究的可行性；多值的模糊邏輯比二值明確邏輯更能夠正確反映出人類的思維。 / The aim of this study was to propose and validate the new scaling method, fuzzy partial credit scaling (FPCS), which combines fuzzy set theory with the partial credit model (PCM) to score rating scales. To achieve this goal, the Chinese version of BDI (Beck Depression Inventory-II) was administrated to a depressed sample of patients and a non-depressed sample. The depressed sample consisted of 240 outpatients who were diagnosed as depressed by a psychiatric doctor, while 321 undergraduate students were recruited for the nondepressed sample. In FPCS, triangular fuzzy numbers were generated by step parameters to characterize distributions of each alternative value. Next, the center of gravity (COG) method was applied to “de-fuzzify” the fuzzy number into a scalar. Then, the “observed fuzzy scores” defined in FPCS were calculated as the sums of fuzzy number values weighted by membership degrees for the following analysis. Three studies were performed to compare the differences in reliability, validity and clustering precision between the raw score and FPCS. In Study One, the reliability issue of FPCS was discussed. The results of confirmatory factor analysis demonstrate that the BDI reliability was higher in FCPS than in raw scoring. That is, compared with raw scoring, scoring via FPCS produced fewer measurement errors, meaning that more variances in an item of BDI were explained by depression. In Study Two, the predictive validity issue of FPCS was investigated. First, logistic regression analysis was used to predict the odds of suffering depression based on FPCS and the raw scores. The analytical results showed that, via FPCS, the probability of correct classification of depressed and non-depressed was raised from 74.8% to 77.2%. Next, discrimination analysis was performed to classify the subjects according to the severity of depression into three categories: non-depression, depression with remission and depression without remission. The analytical results exhibited that, via FPCS, the probability of correct classification of severity of depression was raised from 71.2% to 80.7%. These two statistical analyses consistently show that FPCS exhibited higher predictive validity than did the raw score. That is, BDI scoring via FPCS makes more accuracy predictions for depression than raw score. In Study Three, fuzzy c-means (FCM) clustering was applied to partition the sample according to severity of depression. To examine explore whether fuzzy-based clustering methods uncover the information inherent in the latent structure more accurately than crisp clustering, FCM, Wald’s method, and k-means method were performed. The analytical results reveal that the association between the original and classified membership generated by FCM was stronger than that of the Wald and k-means methods. Hence, FCM revealed the data structure most accurately. Overall, FPCS has been consistently shown to be superior to raw scoring in terms of reliability, validity, and clustering accuracy. This study has empirically shown that fuzzy set theory is applicable to psychological research.

近年來，大型資料庫的建制與分析逐漸成為一種教育研究趨勢，本研究即以PISA 2003資料庫為例，目的是建立影響數學成就的結構方程式模型。在評閱相關文獻後，研究者採用內在動機、工具性動機、數學焦慮、自我概念與數學成就等變項，探討之間的影響關係模型。此外，為使本研究所建立的模型具有模型穩定之證據，因此，將有效樣本隨機分割為建模樣本與驗證樣本，進行最終模型的交叉驗證。 據此，本研究首先使用描述性統計以瞭解香港學生的整體表現傾向，其次，透過探索性因素分析確立研究問卷的信效度，最後，以結構方程式模型建立模型並交叉驗證。資料蒐集對象為香港十五歲之在學學生，有效樣本達4,389位。 依據統計分析結果顯示，內在動機與工具性動機對數學成就沒有直接影響效果，但是內在動機與工具性動機透過數學焦慮及自我概念對數學成就產生間接影響，本研究歸納出七點結論茲分述如下： 1.工具性動機較內在動機更為強烈 2.數學焦慮在動機與數學成就間扮演中介變項之性質 3.自我概念在動機與數學成就間扮演中介角色 4.自我概念在數學焦慮與數學成就間扮演中介角色 5.在內在動機、工具性動機與數學焦慮中，工具性動機扮演負向壓抑變項角色 6.在內在動機、工具性動機與自我概念中，工具性動機扮演負向壓抑變項角色 最後，根據研究結果提出各項建議，以供教學實務上及未來研究參考。 / Recently, establishing and analyzing databases becomes a trend in the field of education research. This study took PISA 2003 database as an example to create a psychometric model of factors that influence mathematics achievement. Based on the literature review, the researcher decided to put influential factors, including intrinsic motivation, instrumental motivation, mathematics anxiety, self-concept, and mathematics achievement into the model. Afterwards, through cross-validation the present study had verified the model stability. In the aspect of statistic analysis, the descriptive static shows HK students’ general learning tendency. Moreover, the exploratory factor analysis confirmed the reliability and validity of the questionnaires. Lastly, the structural equation modeling(SEM) was used to set structural model. The valid samples were 4,389 15-year-old students. According to the results, intrinsic motivation and instrumental motivation had no direct effect on mathematics achievement and had indirect effect through mathematics anxiety and self-concept. The results were summarized as follows: 1.Students had more instrumental motivation than intrinsic one. 2.Mathematics anxiety was a mediator variable between motivations and mathematics achievement. 3.Self-concept was a mediator variable between intrinsic motivations and mathematics achievement. 4.Self-concept was a mediator variable between mathematics anxiety and mathematics achievement. 5.Instrumental motivation was a negative suppressor variable among intrinsic motivation, instrumental motivation, and mathematics anxiety. 6.Instrumental motivation was a negative suppressor variable among intrinsic motivation, instrumental motivation, and self-concept. Finally, according to the findings, implications and suggestions for teaching of mathematics and future research were discussed.

近幾年來，國人自殺死亡率不斷提高，且自殺死亡從1997年起已連續多年列於國人十大死亡原因之一，所以自殺防治工作刻不容緩。本研究採用自殺防治中心在桃園縣六家居家服務單位(龍祥、中國、仁愛、紅十字、家輔及寬福)所做之問卷調查資料，目的在於找出何種特性者，BSRS5 (The Five-Item Brief Symptom Rating Scale)分數及自殺意念分數可能較高。本研究屬於時序性追蹤資料，自民國96年5月份起，由居服人員針對受測對象進行訪談，大約每隔兩週收集一次，總共進行四次。 針對問卷進行基本敘述性統計、單項排名分析以及交叉分析後發現，在人口特質方面，男女性比例相當，年齡層主要皆在65~84歲，教育程度以不識字及國小為主；在BSRS5五題排名方面，以第一題「睡眠困難(難以入睡或早醒)」的平均分數最高，第四題「覺得比不上別人」平均分數最低；由交叉分析的結果發現身體狀況為一個重要的變數，身體狀況差的人BSRS5總分6分以上或自殺意念2分以上明顯較多。 對資料配適廣義估計方程式及Alternating Logistic Regressions的結果，發現在反應變數為BSRS5總分時，女性、身體狀況差及曾經看過精神科者BSRS5分數達到6分以上的可能性較高。若反應變數為自殺意念時，無論是利用廣義估計方程式或Alternating Logistic Regressions，從模型配適的結果發現只有BSRS5的效應顯著。不管利用BSRS5總分或是各題分開來看，BSRS5對自殺意念是一個相當有效的檢測工具，BSRS5分數愈高則自殺意念2分以上的機會也愈高。此外利用多層結構分析方法配適廣義估計方程式，針對BSRS5與受測次數間的關聯性分析，發現與配適傳統unstructured相關性矩陣的估計結果差異不大，但是可以減少許多參數估計，並且在電腦計算時間上是較快速的。 / In Taiwan, suicide has been among the top ten causes of death since 1997, and suicide prevention has thus attracted much attention since. Using the data provided by Taiwan Suicide Prevention Center (TSPC), this study is aimed to find out possible personal characteristics that might have some impacts on the BSRS5 (the Five-Item Brief Symptom Rating Scale) and suicide ideation scores The data come from a longitudinal study in which subjects from six elderly home service centers in Taoyuan County, Taiwan were visited four times between May and July, 2007, about two weeks between each visit. The total number of subjects is 1981. The proportions of male and female are nearly the same, the age range is from 65 to 84, and most of them have only an elementary school degree. Preliminary analyses indicate that among the five items in BSRS5, insomnia (the first item) is ranked the highest, and inferiority (the fourth item) is the lowest. In addition, health status is highly correlated to the BSRS5 and suicide ideation scores, the worse the health status, the higher the BSRS5 and suicide ideation scores. Fitting the data with Generalized Estimating Equation (GEE) and Alternating Logistic Regressions models with respect to the BSRS5 score, we further find that female, those who have bad health status, and those who have ever consulted a psychiatrist have higher probability that the BSRS5 score is greater than 6. As far as the suicide ideation score is concerned, the BSRS5 score is the only covariate that is statistically significant, an indication that BSRS5 is a useful tool for screening subjects at risk of committing suicide. While the conclusions stay the same whether the data are analyzed through GEE with commonly used unstructured correlation structure or newly developed multiblock and multilayer correlation structure, the latter approach reduces the computer time significantly.

在急速變遷與多元渾沌的現今，如何轉化複雜且遽增的壓力以提升個體本身的幸福感實屬一重要的議題。本研究主要目的在建立生活壓力、解釋風格與情緒幸福感的結構方程式模型，藉以探討之間的影響關係，進而瞭解解釋風格在這關係中所扮演的中介效果。 本研究以兩組各644位政治大學的大學生為研究對象，採問卷調查法施以生活壓力量表、解釋風格量表及情緒幸福感量表，使用的資料分析方法包括：t考驗、單因子變異數分析、因素分析、及結構方程式模型。本研究以第一組樣本探究不同性別與不同年級在研究變項上的差異，接著，經建構與修正模式後提出最終的關係模式，最後，以第二組樣本驗證最終模式的穩定性。主要結果茲分述如下： 一、在背景變項方面： (一)不同性別與不同年級大學生在「生活壓力」與「解釋風格」上有顯著差 異。 (二)不同性別與不同年級大學生在「情緒幸福感」上未有顯著差異。 二、在結構模式方面： (一)課業壓力、人際壓力對解釋風格有直接正向效果。 (二)課業壓力、人際壓力對情緒幸福感有直接負向效果。 (三)解釋風格對情緒幸福感有直接負向效果。 (四)人際壓力能直接影響情緒幸福感，也能透過解釋風格間接影響情緒幸福感。 (五)解釋風格在課業壓力與情緒幸福感間扮演完全中介變項的角色。 (六)最終模式的交叉驗證具有模式穩定性。 最後，根據研究結果提出建議，供諮商輔導實務及未來研究參考。 / With the rapid change and the multicultural context of the modern society, how to deal with the complicated and hastily increased stress and to promote people’s well-being is an important issue. The main purpose of this study is to construct the structural equation modeling (SEM) of stress, explanatory style, and emotional well-being. By this way, the researcher can explore the relationship among the three variables, and know the mediator variable of explanatory style. The participants were two groups of students at National Chengchi University, and each group included 644 college students. The data was collected by questionnaires, including the stress scale, the explanatory style scale, and the emotional well-being scale. Moreover, the data were analyzed by t-test, ANOVA, factor analysis, and SEM. The study, firstly, used the first group to explore the differences of gender and grade, and constructed the final structural model after setting and modifying model. Finally, the researcher used the second group to verify the stability of the model. The main results were summarized as follows: About the background variables: 1.Students with different gender and grade were significantly different in the scores of stress and explanatory style. 2.Students with different gender and grade were not significantly different in the scores of emotional well-being. About the structural model: 1.Academic stress and relationship stress had positive influence on explanatory style directly. 2.Academic stress and relationship stress had negative influence on emotional well-being directly. 3.Explanatory style had negative influence on emotional well-being directly. 4.Relationship stress had influence on emotional well-being directly, and it also affected emotional well-being through explanatory style. 5.Explanatory style was a mediator variable between academic stress and emotional well-being. 6.Through the cross-validation, the final structural model was of model stability. Finally, based on the findings of the study, the researcher made some practical strategies for counselor and some suggestions for further studies.

在這篇論文,我們考慮半線性微分方程式的初始邊界值問題之解u,的存在性,唯一性,和他的行為. (i) t^{-sigma}u''(t)=r_1u(t)^p+r_2u(t)^p(u'(t))^2, u(1)=u_0,u'(1)=u_1, 其中 p>1 為常數. 對t≥1,sigma>0,p>1 為偶數,r_1>0,r_2>0,u_0>0,u_1>0. 我們得到以下的結果.

本論文主要目標為發展金融互換的定價模型。既是欲建立量化模型，首要 工作在於對量化對象 --- 金融互換工具的實際特性， 實務上的運作，有 瞭解與掌握，再輔以必要的數量基礎，方不致於`` 失真 '' 。本文共分 五章首章為緒論，第二章為對金融互換工具的全盤認識，試圖由金融互換 的契約切入，進而歸納分類要件，演化及最終種類，最後提出定價時的幾 個思維面向(Dimensions )。第三章為文獻回顧，指出金融互換定價模型 的基礎，為建立在具浮動利率金融工具的定價模型上。 第四章為發展理 論模型基礎及數值分析結果。第五章為結論。

本研究之目的在於瞭解國民小學學生網路使用行為與網路閱讀素養之關係，採問卷調查法收集研究資料，以全臺灣各縣市之國民小學高年級學生為研究母群，進行分層隨機抽樣，共取得有效樣本1182人。 研究工具採用「網路使用行為問卷」、「網路閱讀素養問卷」，並以t 檢定、Pearson積差相關、迴歸分析等方法進行研究資料分析，最後以結構方程式模型建立網路使用行為與網路閱讀素養模型，研究結果如下： 一、性別在資訊瀏覽與搜尋活動、線上遊戲活動方面達顯著差異。 二、性別在整體網路閱讀素養上無顯著差異。 三、年級在訊瀏覽與搜尋活動、社群活動方面達顯著差異，在線上遊戲上無顯著差 異。 四、年級在整體網路閱讀素養上達顯著差異，六年級優於五年級。 五、結構方程式模型檢定資訊瀏覽與搜尋活動、線上遊戲活動對國小學生網路閱 讀素養有顯著的影響。 六、資訊瀏覽與搜尋活動能正向預測網路閱讀素養，線上遊戲對網路閱讀素養有 負向影響，社群活動對網路閱讀素養無顯著影響。 最後，根據研究結果提出各項建議，以供教學實務上及未來參考。 / This research aims to reveal the relationship between internet usage behavior and internet reading literacy of elementary school students. This study used a questionnaire survey method to collect data. The subjects were collected from the elementary school students in 2011 by the stratified random sampling. The total valid samples were 1182. The research instruments used in this study included "Internet Usage Behavior Questionnaire", and "Internet Reading literacy Questionnaire ". Meanwhile, the collected data were analyzed by descriptive statistic, the t-test and Pearson correlation and regression analysis. Lastly, data were analyzed with Internet Usage Behavior and Internet Reading Literacy by structural equation modeling. The main findings were as follows: 1.There existed gender differences on information browsing and search activities and online game. 2.There existed no gender differences on internet reading literacy. 3.There existed grade differences on information browsing and search activities, community activities, and no grade differences on online game. 4.There existed grade differences on internet reading literacy with girls performed better than boys. 5.Structural equation modeling (SEM) showed that information browsing and search activities and online game activities had a remarkable influence on the internet reading literacy of elementary school students. 6.The study had found that information browsing and search activities have a positive effect upon internet reading literacy, and online game have a negative effect upon internet reading literacy. Community activities had no influence on the internet reading literacy. Finally, according to the findings, implications and suggestions for teaching and future researches were discussed and proposed.

科学研究費補助金 研究種目:基盤研究(A)(1) 課題番号:11304004 研究代表者:三井 斌友 研究期間:1999-2001年度

This paper explores the interrelationship between the net interest margin (NIM) and noninterest income and their determinants for banks in 9 Asian countries over the period 1998-2010. A simultaneous equations system is used to deal with endogenous regressors and its structural parameters are identified under a heteroskedastic covariance restriction, proposed by Lewbel (2012). The renovated Lerner Index proposed by Huang et al. (2013) is factored as a more robust proxy for market power over HHI. Our results demonstrate significantly positive relationship between the NIM and noninterest income, suggesting overall benefits for banks from income diversification. In addition, the loss-leader behavior is not supported in the sample countries.

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