Search

Copyright of Canadian Journal of Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article offers reflections on the development of the Rubin causal model (RCM), which were stimulated by the impressive discussions of the RCM and Campbell's superb contributions to the practical problems of drawing causal inferences written by Will Shadish (2010) and Steve West and Felix Thoemmes (2010). It is not a rejoinder in any real sense but more of a sequence of clarifications of parts of the RCM combined with some possibly interesting personal historical comments, which I do not think can be found elsewhere. Of particular interest in the technical content, I think, are the extended discussions of the stable unit treatment value assumption, the explication of the variety of definitions of causal estimands, and the discussion of the assignment mechanism. (Contains 3 footnotes.)

Missing data, especially when coupled with noncompliance, are a challenge even in the setting of randomized experiments. Although some existing methods can address each complication, it can be difficult to handle both of them simultaneously. This is true in the example of the New York City School Choice Scholarship Program, where both the covariates and the outcomes were sometimes missing, and there was complicated noncompliance. The authors propose a modified general location model to integrate the ideas of missing data techniques and principal stratification and then analyze the same data as in Barnard, Frangakis, Hill, and Rubin (2003), where a pattern-mixture model was used. Their results are presented and compared with those in Barnard et al. (Contains 10 tables.)

An approach to handle partial compliance behavior using principal stratification is presented and applied to a subset of the longitudinal data from the New York City School Choice Scholarship Program, a randomized experiment designed to assess the effects of private schools versus public schools on academic achievement. The initial analysis suggests an interesting relationship between compliance with the offer and academic achievement, including a possible "beneficial rejected offer" effect and a possible "adjustment hardship" effect. These results seem to favor public schools in the sense they suggest that the collection of students who would attend private school when offered the scholarship but attend public school without the offer had a lower average posttest score if they attended private school than if they attended public school. This case study illustrates the strengths of principal stratification: the explicit examination of specific assumptions and directly interpretable results with possible policy implications. (Contains 9 tables and 2 figures.)

When estimating causal effects from observational data, it is desirable to approximate a randomized experiment as closely as possible. This goal can often be achieved by choosing a subsample from the original control group that matches the treatment group on the distribution of the observed covariates. However, sometimes the original control group cannot provide adequate matches for the treatment group. This article presents a method to obtain matches from multiple control groups. In addition to adjusting for differences in observed covariates between the groups, the method adjusts for a group effect that distinguishes between the control groups. This group effect captures the additional otherwise unobserved differences between the control groups, beyond that accounted for by the observed covariates. The method is illustrated and evaluated using data from an evaluation of a school drop-out prevention program that uses matches from both local and nonlocal control groups. (Contains 5 figures, 5 tables, and 1 note.)