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An Empirical Bayes Approach to Estimating Ordinal Treatment Effect

Alvarez, R. Michael and Bailey, Delia and Katz, Jonathan N. (2011) An Empirical Bayes Approach to Estimating Ordinal Treatment Effect. Political Analysis, 19 (1). pp. 20-31. ISSN 1047-1987. doi:10.1093/pan/mpq033.

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Ordinal variables—categorical variables with a defined order to the categories, but without equal spacing between them—are frequently used in social science applications. Although a good deal of research exists on the proper modeling of ordinal response variables, there is not a clear directive as to how to model ordinal treatment variables. The usual approaches found in the literature for using ordinal treatment variables are either to use fully unconstrained, though additive, ordinal group indicators or to use a numeric predictor constrained to be continuous. Generalized additive models are a useful exception to these assumptions. In contrast to the generalized additive modeling approach, we propose the use of a Bayesian shrinkage estimator to model ordinal treatment variables. The estimator we discuss in this paper allows the model to contain both individual group–level indicators and a continuous predictor. In contrast to traditionally used shrinkage models that pull the data toward a common mean, we use a linear model as the basis. Thus, each individual effect can be arbitrary, but the model ‘‘shrinks’’ the estimates toward a linear ordinal framework according to the data. We demonstrate the estimator on two political science examples: the impact of voter identification requirements on turnout and the impact of the frequency of religious service attendance on the liberality of abortion attitudes.

Item Type:Article
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URLURL TypeDescription
Alvarez, R. Michael0000-0002-8113-4451
Katz, Jonathan N.0000-0002-5287-3503
Additional Information:© 2010 The Author. Published by Oxford University Press on behalf of the Society for Political Methodology. Advance Access publication December 30, 2010.
Issue or Number:1
Record Number:CaltechAUTHORS:20140314-120454857
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:44317
Deposited By: Jonathan Katz
Deposited On:17 Mar 2014 21:05
Last Modified:10 Nov 2021 16:50

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