巢式羅機模式與效用最大理論的關係

Nested Logit Models and Random Utility Maximization

本研究探討隨機效用最大理論與兩種常用的巢式羅機模式間的關係，這兩種模式分別是非標準化巢式羅機模式與效用最大巢式羅機模式。本文以顯示隨機偏好公理檢驗非標準化巢式羅機模式是否滿足全域效用最大理論，並以圖形描繪非標準化巢式羅機模式滿足區域效用最大理論的空間位置。本文亦討論了四種會使巢式羅機模式出現錯誤而得出不相似指標大於1的數據，並提出解決此問題的數種因應辦法，如貝氏巢式羅機模式與可容許方案異質與相似的一般化極端值模式等。

This paper 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. This paper examines 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 paper also explores four scenarios where nested logit models may wrongly obtain large dissimilarity parameters. We suggested several methods to deal with this problem, for example, Bayesian UMNL and flexible GEV model which could allow correlation and heteroscedasticity among alternatives.