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Interaction Terms in Nonlinear Models

Authors

  • Pinar Karaca-Mandic,

    Corresponding author
    1. Division of Health Policy and Management, School of Public Health, University of Minnesota, Minneapolis, MN
    • Address correspondence to Pinar Karaca-Mandic, Ph.D., Assistant Professor, Division of Health Policy and Management, School of Public Health, University of Minnesota, 420 Delaware Street SE, MMC729, Minneapolis, MN 55455; e-mail: pkmandic@umn.edu.

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  • Edward C. Norton,

    1. Department of Health Policy and Management, Department of Economics, School of Public Health, University of Michigan, Ann Arbor, MI
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  • Bryan Dowd

    1. Division of Health Policy and Management, School of Public Health, University of Minnesota, Minneapolis, MN
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Abstract

Objectives

To explain the use of interaction terms in nonlinear models.

Study Design

We discuss the motivation for including interaction terms in multivariate analyses. We then explain how the straightforward interpretation of interaction terms in linear models changes in nonlinear models, using graphs and equations. We extend the basic results from logit and probit to difference-in-differences models, models with higher powers of explanatory variables, other nonlinear models (including log transformation and ordered models), and panel data models.

Empirical Application

We show how to calculate and interpret interaction effects using a publicly available Stata data set with a binary outcome. Stata 11 has added several features which make those calculations easier. LIMDEP code also is provided.

Conclusions

It is important to understand why interaction terms are included in nonlinear models in order to be clear about their substantive interpretation.

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