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Attributable Effects and Full Matching for Binary Outcomes in Field Experiments and Observational Studies

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Abstract:

Statistical analysis requires a probability model: commonly, a model
for the dependence of outcomes $Y$ on confounders $X$ and a
potentially causal variable $Z$. When the goal of the analysis is to
infer $Z$'s effects on $Y$, this requirement introduces an element
of circularity: in order to decide how $Z$ affects $Y$, the analyst
first determines, speculatively, the manner of $Y$'s dependence on
$Z$ and other variables. This paper takes a statistical perspective
that avoids such circles, permitting analysis of $Z$'s effects on
$Y$ even as the statistician remains entirely agnostic about the
conditional distribution of $Y$ given $X$ and $Z$, or perhaps even
denies that such a distribution exists. Our assumptions instead
pertain to the conditional distribution $Z \vert X$, and the role of
speculation in settling them is reduced by the existence of random
assignment of $Z$ in a field experiment as well as by
poststratification, testing for overt bias before accepting a
poststratification, and optimal full matching. Such beginnings pave
the way for ``randomization inference'', an approach which, despite
a long history in the analysis of designed experiments, is
relatively new to political science and to other fields in which
experimental data are rarely available.

The approach applies to both experiments and observational studies.
We illustrate this by applying it to analyze A. Gerber and
D. Green's New Haven Vote 98 campaign. Conceived as both a
get-out-the-vote campaign and a field experiment in political
participation, the study assigned households to treatment and
desired to estimate the effect of treatment on the individuals
nested within the households. We estimate the number of voters who
would not have voted had the campaign not prompted them to --- that
is, the total number of votes attributable to the interventions of
the campaigners --- while taking into account the non-independence
of observations within households, non-random compliance, and
missing responses. Both our statistical inferences about these
attributable effects and the stratification and matching that
precede them rely on quite recent developments from statistics; our
matching, in particular, has novel features of potentially wide
applicability. Our broad findings resemble those of the original
analysis by \citet{gerbergreen00}.

Most Common Document Word Stems:

treatment (205), 1 (164), vote (137), c (116), match (115), z (105), ect (103), assign (101), e (101), y (93), q (90), random (87), 2 (87), m (78), control (74), subject (74), n (73), attribut (68), number (67), one (63), yi (60),

Author's Keywords:

randomization inference, experiments, field experiments, political participation, statistics, matching
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Association:
Name: American Political Science Association
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MLA Citation:

Bowers, Jake. and Hansen, Ben. "Attributable Effects and Full Matching for Binary Outcomes in Field Experiments and Observational Studies" Paper presented at the annual meeting of the American Political Science Association, Marriott Wardman Park, Omni Shoreham, Washington Hilton, Washington, DC, Sep 01, 2005 <Not Available>. 2008-10-09 <http://www.allacademic.com/meta/p40212_index.html>

APA Citation:

Bowers, J. and Hansen, B. , 2005-09-01 "Attributable Effects and Full Matching for Binary Outcomes in Field Experiments and Observational Studies" Paper presented at the annual meeting of the American Political Science Association, Marriott Wardman Park, Omni Shoreham, Washington Hilton, Washington, DC Online <APPLICATION/PDF>. 2008-10-09 from http://www.allacademic.com/meta/p40212_index.html

Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: Statistical analysis requires a probability model: commonly, a model
for the dependence of outcomes $Y$ on confounders $X$ and a
potentially causal variable $Z$. When the goal of the analysis is to
infer $Z$'s effects on $Y$, this requirement introduces an element
of circularity: in order to decide how $Z$ affects $Y$, the analyst
first determines, speculatively, the manner of $Y$'s dependence on
$Z$ and other variables. This paper takes a statistical perspective
that avoids such circles, permitting analysis of $Z$'s effects on
$Y$ even as the statistician remains entirely agnostic about the
conditional distribution of $Y$ given $X$ and $Z$, or perhaps even
denies that such a distribution exists. Our assumptions instead
pertain to the conditional distribution $Z \vert X$, and the role of
speculation in settling them is reduced by the existence of random
assignment of $Z$ in a field experiment as well as by
poststratification, testing for overt bias before accepting a
poststratification, and optimal full matching. Such beginnings pave
the way for ``randomization inference'', an approach which, despite
a long history in the analysis of designed experiments, is
relatively new to political science and to other fields in which
experimental data are rarely available.

The approach applies to both experiments and observational studies.
We illustrate this by applying it to analyze A. Gerber and
D. Green's New Haven Vote 98 campaign. Conceived as both a
get-out-the-vote campaign and a field experiment in political
participation, the study assigned households to treatment and
desired to estimate the effect of treatment on the individuals
nested within the households. We estimate the number of voters who
would not have voted had the campaign not prompted them to --- that
is, the total number of votes attributable to the interventions of
the campaigners --- while taking into account the non-independence
of observations within households, non-random compliance, and
missing responses. Both our statistical inferences about these
attributable effects and the stratification and matching that
precede them rely on quite recent developments from statistics; our
matching, in particular, has novel features of potentially wide
applicability. Our broad findings resemble those of the original
analysis by \citet{gerbergreen00}.

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Abstract Only All Academic Inc.
Associated Document Available American Political Science Association
Associated Document Available Political Research Online

Document Type: application/pdf
Page count: 41
Word count: 20008
Text sample:
Attributing Effects to A Cluster Randomized Get-Out-The-Vote Campaign: An Application of Randomization Inference Using Full Matching∗ Jake Bowers and Ben Hansen Political Science and Statistics University of Michigan jwbowers@umich.edu and bbh@umich.edu July 18 2005 Abstract Statistical analysis requires a probability model: commonly a model for the dependence of outcomes Y on confounders X and a potentially causal variable Z. When the goal of the analysis is to infer Z’s effects on Y this requirement introduces an element of circularity:
Sensitivity in Obser- vational Studies ” The American Statistician 59 147–152. Rosenstone S. and Hansen J. M. (1993) Mobilization Participation and Democracy in Amer- ica MacMillan Publishing. Rubin D. B. (1986) “Comments on “Statistics and Causal Inference” ” Journal of the American Statistical Association 81 961–962. Verba S. Schlozman K. L. and Brady H. (1995) Voice and Equality: Civic Voluntarism in American Politics Cambridge: Harvard University Press. Walter S. D. (1976) “The estimation and interpretation of attributable risk in


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