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The discounted logit is widely used to estimate time preferences using data from field and laboratory experiments. Despite its popularity, it exhibits the "problem of the scale": choice probabilities depend on the scale of the value function. When applied to intertemporal choice, the problem the scale implies that logit probabilities are sensitive to the temporal distance between the choice and the outcomes. This is a failure of an intuitive requirement of stationarity although future values are discounted geometrically. As a consequence, patterns of choice following from the structure of the logit may be attributed to non-stationary discounting. We solve this problem introducing the discounted Luce rule. It retains the flexibility and simplicity of the logit while it satisfies stationarity. We characterize the model in two settings: dated outcomes and consumption streams. Relaxations of stationarity give observable restrictions characterizing hyperbolic and quasi-hyperbolic discounting. Lastly, we discuss an extension of the model to recursive stochastic choices with the present bias.

This book is designed as a gentle introduction to the fascinating field of choice modeling and its practical implementation using the R language. Discrete choice analysis is a family of methods useful to study individual decision-making. With strong theoretical foundations in consumer behavior, discrete choice models are used in the analysis of health policy, transportation systems, marketing, economics, public policy, political science, urban planning, and criminology, to mention just a few fields of application. The book does not assume prior knowledge of discrete choice analysis or R, but instead strives to introduce both in an intuitive way, starting from simple concepts and progressing to more sophisticated ideas. Loaded with a wealth of examples and code, the book covers the fundamentals of data and analysis in a progressive way. Readers begin with simple data operations and the underlying theory of choice analysis and conclude by working with sophisticated models including latent class logit models, mixed logit models, and ordinal logit models with taste heterogeneity. Data visualization is emphasized to explore both the input data as well as the results of models. This book should be of interest to graduate students, faculty, and researchers conducting empirical work using individual level choice data who are approaching the field of discrete choice analysis for the first time. In addition, it should interest more advanced modelers wishing to learn about the potential of R for discrete choice analysis. By embedding the treatment of choice modeling within the R ecosystem, readers benefit from learning about the larger R family of packages for data exploration, analysis, and visualization.