Modeling and Analysis of Discrete Response Data: Applications to Public Opinion on Marijuana Legalization in the United States

TL;DR

This paper reviews discrete choice models for limited dependent variables, connects them to economic utility theory, discusses estimation and model assessment, and applies these models to analyze US public opinion on marijuana legalization, revealing key influencing factors.

Contribution

It provides a comprehensive overview of discrete choice models, connects them to economic theory, and applies them to a socially relevant issue, offering new insights into public opinion determinants.

Findings

Past marijuana use influences opinion

Beliefs about legalization affect attitudes

Political partisanship shapes public views

Abstract

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.