Choice-based sampling selects a population conditional on the choices it has made. By allowing the sampling rate to be dependent on choice, certain outcomes can be sampled at higher or lower rates than occurring in the population, and can assure obtaining sufficient observations to conduct an empirical analysis of choice. Samples formed on the basis of choice can produce consistent estimates of the population making a particular choice by using weights. This paper defines the weights, demonstrates their role in estimating the population subgroup making a particular choice, and gives a theorem in the use of weights in maximum likelihood estimation of a choice equation. This theorem greatly enhances the usefulness of choice-based samples in empirical work and, in a special case of the theorem, the conditional logit model, consistent estimates of all parameters except the intercept terms can be obtained from "raw" choice-based data, without weighting.
This report is part of the RAND Corporation Paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.
Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit www.rand.org/about/principles.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.