本論文研究重點在於離散選擇模式方案異質與相似的誤差項課題上，可分為三部分：

　　首先將說明過去離散選擇模式相關文獻，在處理方案異質性與相似性時的缺失，以及隱含的可能問題。除了以數學式、理論說明外，並採用模擬實驗輔助說明。在方案異質性部分，說明「方案異質性」與「方案乘數效果」兩種可能混淆的異質性問題，在方案相似性部分，提出巢層搜尋法的缺失，以及說明羅機核心模式處理相似時，可能引發更嚴重的方案異質問題。本研究提出來的數種離散選擇模式的謬誤問題，均可作為相關研究的參考，以避免錯誤的推論。

　　其次，將探討兩種截然不同的巢式羅機模式與效用最大理論的關係。本研究除了解決「非標準化巢式羅機模式」多年懸而未決的效用最大理論爭議，並提出全域與區域兩種效用最大理論。而後針對「效用最大巢式羅機模式」，說明四種可能造成「不相似指標大於一」特性的數據，及提出修正方法與看待角度。另外，本研究從理論以及模擬實驗解釋兩種巢式羅機模式雖可以描述相同的數據，但是在描述數據的空間座標軸並不一致，此一特性為導致兩模型採用相同效用函數的設計卻可能有不同的結果。

　　最後，以貝氏統計觀點探討兩種最常使用的個體選擇模式：巢式羅機模式，以及常機模式，討論的主題包括貝氏統計的模型設計，先驗知識扮演的角色以及誤差項參數認定方法，並輔以模擬實驗，以茲驗證。在貝氏巢式羅機模式的論述與實驗中，著重與比較不同先驗知識，透過先驗分佈，討論對貝氏估計值的影響。在常機模式部分，針對誤差項參數認定議題，本研究以「向量長度固定」觀點出發，提出另一種參數認定方法。文中並以實驗數據比較數種認定方法，結果顯示本研究發展的參數認定方法，在演算法速度與統計特性均有不錯的表現。

　This dissertation is concerned with the error terms of correlated and heteroscedastic alternatives in discrete choice models. Contributions are made to three key aspects including:

　Flexible discrete choice models such as logit kernel, nested logit and heteroscedastic extreme value models are used widely to handle correlation and heteroscedasticity among alternatives in a variety of fields such as transportation, economics and marketing. However, lots of literatures misinterpret correlated and heteroscedastic alternatives by improper models. This study presents the consequence of mistaking improper models with theorectical interpretations and simulation experiments.

　First, two types of heteroscedasticity are often confused due to similar function forms though there are two distinct explanations for both. One is caused by the unobserved error terms with different degrees of variances and the other one is simply the alternative multiplier effect. We term the former case ture heteroscedasticity among alternative and the latter case spurious heteroscedasticity. We show that two types of heteroscedasticity without discriminating from each other might lead to incorrect statistical inference.

　Second, two issues about correlation are discussed. One issue is about HEV search engine, a method of specifying nested logit tree structure. Conditions, which the HEV search method is unable to tackle, are demonstrated in order to well know cons and pros of the method and get better tree structures. The other issue states a potential dilemma while logit kernel model is applied to handle correlation between alternatives with factor analytic structure. This paper illustrates the correct way to estimate the correlation and heteroscedasticity by Monte Carlo experiments and theoretical proofs. These insights could be practically useful for studies of economic choices to better understand consumer behavior.

　Moreover, this dissertation investigates the relationships between random utility maximization (RUM) and two widely used nested logit models, i.e., non-normalized nested logit (NNNL) model and utility maximization nested logit (UMNL) model. We examines the controversial issue, whether NNNL model satisfies the global consistency of RUM, with axiom of revealed stochastic preference. A graphical analysis is introduced to illustrate possible local consistency area for NNNL model.

　This study also explores four scenarios where UMNL may wrongly obtain large dissimilarity parameters. Several corresponding methods are suggested to deal with the problem. For example, Bayesian UMNL and flexible GEV model which could allow correlation and heteroscedasticity among alternatives are introduced.

　Bayesian statistics have made great improvement in recent years due to the development of simulation method known as Markov chain Monte Carlo (MCMC). This paper reviews the underlying Bayesian statistical concepts and the state-of-the-art Bayesian modeling approaches for two popular discrete choice models, i.e., nested logit model and multinomial probit model. This study demonstrates the role of priors, identification and computational issues relating to Gibbs sampler and Metropolis-Hasting algorithm via Monte Carlo experiments. In particular, we introduce a new MCMC algorithm for Bayesian analysis of multinomial probit model. The results show that this new algorithm has good performance and statistic properties without complex coding.

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