Interaction terms in nonlinear models

Health Serv Res. 2012 Feb;47(1 Pt 1):255-74. doi: 10.1111/j.1475-6773.2011.01314.x. Epub 2011 Aug 30.


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.

MeSH terms

  • Age Factors
  • Data Interpretation, Statistical
  • Female
  • Humans
  • Male
  • Multivariate Analysis*
  • Nonlinear Dynamics*
  • Odds Ratio
  • Probability
  • Sex Factors