Statistical and Mathematical Models of Choice

The following are materials related to my research on choice behavior. Currently there are three major parts to this project:

1) Statistical Models of Crisis Bargaining Games, which focuses the decision of players (e.g., individuals, heads of state, military leaders) to engage in conflict

2) Models of Intertemporal Choice, which focuses on how individuals learn over time and make transitions between choices

3) How individuals respond to discrete choices in surveys, which focuses on to compare individuals who use a different metric in responding to survey responses; my interest currently lies in the practice of using "anchoring" vignettes.

Papers

Comparing Models of Strategic Choice: The role of uncertainty and signaling
Jonathan Wand. 2005. Political Analysis

Testing the fit of competing equilibrium solutions to extensive form games crucially depends on assumptions about the distribution of player types. To illustrate the importance of these assumptions for differentiating between standard statistical models of strategic choice, I draw on a game previously analyzed by Lewis and Schultz (2003). The differences that they highlight between a pair of Perfect Bayesian Equilibrium (PBE) and Quantal Response Equilibrium (QRE) models are not produced by signaling and updating dynamics as claimed, but are instead produced by different assumptions about the distribution of player types. The method of analysis developed and the issues raised are applicable to a broad range of structural models of conflict and bargaining.

Models of Intertemporal Choice

In this paper, I consider the behavior of individuals making repeated choices over a finite set of discrete alternatives. Individuals are assumed to maximize utility each time they are faced with a choice, without affecting the utility or availability of future choices. I build on a class of models where serial correlation in choices is due to a process of learning over time about the merits of alternatives, rather than due to unobserved persistent effects. I provide new analytical results for characterizing transition probabilities between choices without imposing restrictions on how the systematic component of utilities may change over time.

Related graduate course

POLISCI 350C, including syllabus, notes and problems sets

This course primarily considers mathematical and statistical models of individual choice behavior. Emphasis will be placed both on the derivations and motivations for statistical models of choice. Empirical applications will be reviewed to motivate and illustrate different models. Readings will be from political science, mathematical psychology, econometrics, statistics, and sociology. Topics include multinomial choice models and extensions, including strategic choice, dynamic choice, and the modeling of aggregated choices. Maximum likelihood will be the primary method of estimation considered, with a brief overview of simulation methods in a classical framework.

Related software

Anchors: Software for Anchoring Vignettes

Anchors is a complete library of statistical functions for analyzing survey data with anchoring vignettes. The software runs on both MS-windows and linux, and can be used either with a graphical user interface (GUI) which assumes no coding by the user, as well as an extensible R library.