This chapter presents an overview of a specific form of limited dependent variable models, namely discrete choice models, where the dependent (response or outcome) variable takes values which are discrete, inherently ordered, and characterized by an underlying continuous latent variable. Within this setting, the dependent variable may take only two discrete values (such as 0 and 1) giving rise to binary models (e.g., probit and logit models) or more than two values (say $j=1,2, \ldots, J$, where $J$ is some integer, typically small) giving rise to ordinal models (e.g., ordinal probit and ordinal logit models). In these models, the primary goal is to model the probability of responses/outcomes conditional on the covariates. We connect the outcomes of a discrete choice model to the random utility framework in economics, discuss estimation techniques, present the calculation of covariate effects and measures to assess model fitting. Some recent advances in discrete data modeling are also discussed. Following the theoretical review, we utilize the binary and ordinal models to analyze public opinion on marijuana legalization and the extent of legalization -- a socially relevant but controversial topic in the United States. We obtain several interesting results including that past use of marijuana, belief about legalization and political partisanship are important factors that shape the public opinion.

翻译：本章概述了特定形式的受限因变量模型，即离散选择模型。在此类模型中，因变量（响应或结果变量）取离散值，这些值具有内在顺序性，并由潜在的连续潜变量刻画。在此框架下，因变量可仅取两个离散值（如0和1），由此产生二元模型（例如probit和logit模型）；或取两个以上值（如$j=1,2, \ldots, J$，其中$J$为某个通常较小的整数），由此产生有序模型（例如有序probit和有序logit模型）。这些模型的核心目标是在给定协变量的条件下，对响应/结果的概率进行建模。我们将离散选择模型的结果与经济学的随机效用框架相联系，讨论估计方法，介绍协变量效应的计算以及模型拟合的评估指标。此外，还探讨了离散数据建模领域的最新进展。在理论综述之后，我们采用二元模型和有序模型分析美国社会层面具有相关性但颇具争议的话题——公众对大麻合法化及其合法化程度的舆论。研究得出若干有趣的结论，包括大麻过往使用经历、对合法化的认知以及政治党派倾向是塑造公众舆论的重要因素。