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An Empirical Bayes Approach to Estimating Ordinal Treatment Effects

  • R. Michael Alvarez (a1), Delia Bailey (a2) and Jonathan N. Katz (a1)
Abstract

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.

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Corresponding author
e-mail: rma@hss.caltech.edu (corresponding author)
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

J. Aitchison , and S. D. Silvey 1957. The generalization of probit analysis to the case of multiple responses. Biometrika 44: 131–40.

Nathaniel Beck , and Simon Jackman . 1998. Beyond linearity by default: Generalized additive models. American Journal of Political Science 42: 596627.

G. S. Maddala 1983. Limited-Dependent and Qualitative Variables in Econometrics. Cambridge: Cambridge University Press.

Lucky M. Tedrow , and E. R. Mahoney 1979. Trends in attitudes toward abortion: 1972-1976. Public Opinion Quarterly 43: 181–89.

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Political Analysis
  • ISSN: 1047-1987
  • EISSN: 1476-4989
  • URL: /core/journals/political-analysis
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