In this study, we generalize our previous q-generalized multinomial logit model (Nakayama & Chikaraishi, 2015), in which the heteroscedastic variance and flexible shape of the utility distribution are considered, by allowing for statistical dependency of alternatives. This is achieved by introducing the q-generalization of McFadden’s multivariate Gumbel distribution. Thus, the logit model is doubly generalized; 1) each utility follows the generalized extreme value distribution that includes the Gumbel, Weibull, and Fréchet distributions; and 2) the utility distribution is multivariate, and therefore, a nested or cross-nested structure and dependency of alternatives are allowed. The proposed doubly generalized logit model system allows for deriving new closed-form discrete choice models such as the q-generalized nested logit model and q-generalized cross-nested logit (CNL) model. Furthermore, the model system includes conventional logit models such as the multinomial logit, nested logit, and CNL models as special cases as well as the new generalized logit models, while retaining a closed-form expression. We empirically confirm that the goodness-of-fit of the proposed model could be substantially better compared to that of the conventional models in some cases, though the degree of improvements varies across cases.

在这项研究中，我们概括了我们之前的q广义多项式 logit 模型（Nakayama 和 Chikaraishi，2015），其中考虑了效用分布的异方差和灵活形状，允许替代方案的统计依赖性。这是通过引入q来实现的- McFadden 多元 Gumbel 分布的推广。因此，logit 模型是双重泛化的；1) 每个效用遵循广义极值分布，包括 Gumbel、Weibull 和 Fréchet 分布；2) 效用分布是多元的，因此允许嵌套或交叉嵌套的结构和替代方案的依赖。提出的双重广义 logit 模型系统允许推导出新的封闭形式离散选择模型，例如q广义嵌套 logit 模型和q-广义交叉嵌套逻辑（CNL）模型。此外，模型系统包括常规的logit模型，如多项式logit、嵌套logit和CNL模型作为特例，以及新的广义logit模型，同时保留了封闭形式的表达式。我们凭经验证实，在某些情况下，所提出模型的拟合优度可能比传统模型要好得多，尽管改进程度因情况而异。