為探討台灣有線電視收視戶對「分級付費制度」之接受意願，本文參考相關文獻，建立台灣有線電視收視戶對「分級付費制度」接受意願的邏輯式模型（logit model），並採用中央通訊社於2000年8月針對台灣有線電視收視戶進行電話訪查之調查資料進行實證分析，先以圖表進行交叉分析，再進行邏輯式迴歸分析，探討消費者人口統計變數（如性別、教育程度等）、收視行為資料（如每日收看有線電視時數、最常收看頻道數等）對「分級付費制度」接受意願之影響程度。依實證結果，男性、教育程度較高、年齡較大、每日收看有線電視時數較低、收看頻道數目較少及目前繳交有線電視費用較高之收視戶，較有意願接受「分級付費制度」。 / To analyze Taiwan cable TV viewers’ willingness to accept the tiering system, this study first attempts to build a theoretical model of cable TV viewers’ willingness to accept the tiering system based on prior related researches. Secondly, this study applies the logit model to estimate cable TV viewers’ willingness to accept the tiering system based on Central News Agency (CNA) 2000 survey data of cable TV viewers. The empirical results show that male viewers are more willing to accept the tiering system than female. Besides, age, education and current monthly cable TV fee have significantly positive impact on cable TV viewers’ willingness to accept the tiering system while daily watching hours and the number of channels viewed have significantly negative impacts.

本文主要在探討自變數存在有測量誤差時，邏輯式迴歸模型的估計問題，並設計實驗使得測量誤差能滿足遞減假設，進一步應用序貫分析方法，在給定水準下，建立一個信賴範圍。 當自變數存在有測量誤差時，通常會得到有偏誤的估計量，進而在做決策時會得到與無測量誤差所做出的決策不同。在本文中提出了一個遞減的測量誤差，使得滿足這樣的假設，可以證明估計量的強收斂，並證明與無測量誤差所得到的估計量相同的近似分配。相較於先前的假設，特別是證明大樣本的性質，新增加的樣本會有更小的測量誤差是更加合理的假設。我們同時設計了一個實驗來滿足所提出遞減誤差的條件，並利用序貫設計得到一個更省時也節省成本的處理方法。 一般的case-control實驗，自變數也會出現測量誤差，我們也證明了斜率估計量的強收斂與近似分配的性質，並提出一個二階段抽樣方法，計算出所需的樣本數及建立信賴區間。 / In this thesis, we focus on the estimate of unknown parameters, experimental designs and sequential methods in both prospective and retrospective logistic regression models when there are covariates measured with errors. The imprecise measurement of exposure happens very often in practice, for example, in retrospective epidemiology studies, that may due to either the difficulty or the cost of measuring. It is known that the imprecisely measured variables can result in biased coefficients estimation in a regression model and therefore, it may lead to an incorrect inference. Thus, it is an important issue if the effects of the variables are of primary interest. When considering a prospective logistic regression model, we derive asymptotic results for the estimators of the regression parameters when there are mismeasured covariates. If the measurement error satisfies certain assumptions, we show that the estimators follow the normal distribution with zero mean, asymptotically unbiased and asymptotically normally distributed. Contrary to the traditional assumption on measurement error, which is mainly used for proving large sample properties, we assume that the measurement error decays gradually at a certain rate as there is a new observation added to the model. This kind of assumption can be fulfilled when the usual replicate observation method is used to dilute the magnitude of measurement errors, and therefore, is also more useful in practical viewpoint. Moreover, the independence of measurement error and covariate is not required in our theorems. An experimental design with measurement error satisfying the required degenerating rate is introduced. In addition, this assumption allows us to employ sequential sampling, which is popular in clinical trials, to such a measurement error logistic regression model. It is clear that the sequential method cannot be applied based on the assumption that the measurement errors decay uniformly as sample size increasing as in the most of the literature. Therefore, a sequential estimation procedure based on MLEs and such moment conditions is proposed and can be shown to be asymptotical consistent and efficient. Case-control studies are broadly used in clinical trials and epidemiological studies. It can be showed that the odds ratio can be consistently estimated with some exposure variables based on logistic models (see Prentice and Pyke (1979)). The two-stage case-control sampling scheme is employed for a confidence region of slope coefficient beta. A necessary sample size is calculated by a given pre-determined level. Furthermore, we consider the measurement error in the covariates of a case-control retrospective logistic regression model. We also derive some asymptotic results of the maximum likelihood estimators (MLEs) of the regression coefficients under some moment conditions on measurement errors. Under such kinds of moment conditions of measurement errors, the MLEs can be shown to be strongly consistent, asymptotically unbiased and asymptotically normally distributed. Some simulation results of the proposed two-stage procedures are obtained. We also give some numerical studies and real data to verify the theoretical results in different measurement error scenarios.