Interaction effect

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In statistical methods, an interaction effect describes the non-additive effects of two or more independent variables in a probability model . This means that for the set of events represented by the observation space, it is assumed that the effect of the characteristics of one of these variables depends on the characteristics of the other variable (s).

The effect of the interaction is characterized by the fact that the effect goes beyond the individual main effects of the variables involved. If only 2 variables are involved in the interaction, one speaks of a two-way interaction or first-order interaction . If the interaction between 3 variables is examined, one speaks of a three-way interaction or interaction of the 2nd order , etc. In general, interactions of a higher order are difficult to interpret, which is why only 1st order interactions are usually taken into account in statistical models. When interpreting such models, care must be taken to interpret the interaction first and then the main effects - the interaction therefore always forms the most valuable effect of a model.

Traditionally, interaction effects are modeled using product terms of the affected variables, but mostly - at least in the social sciences - more complex interactions are more realistic.

In a simple regression analysis with two independent variables x 1 and x 2 , for example, a product term of the type x 1 x 2 would be inserted into the regression equation, so that the complete equation:

would be, where β 3 would indicate the strength of the interaction effect ( α represents the intercept and ξ the error term ). The main effects β1 and β2 can then only be interpreted to a limited extent, one also speaks of conditional main effects.

In general, a distinction is made between ordinal , hybrid and disordinate interactions . For interpretation, it is recommended to create so-called line diagrams that graphically illustrate the interaction.

A simple application example of an interaction effect in an analysis of variance from political science research would be the influence of the gender of an election candidate on the willingness of his supporters to donate, taking into account the gender of the supporters: On average, female supporters might be less willing to donate than men, but they might be more willing to donate to female candidates , while this would decrease for male supporters for female candidates. So there would be an interaction effect between the gender of the supporter and the gender of the candidate.

See also

supporting documents

  1. ^ Southwood, Kenneth E. 1978. "Nouns Theory and Statistical Interaction: Five Models". American Journal of Sociology 83 (5): 1154-1203. P. 1155; doi : 10.1086 / 226678 JSTOR 2778190 .
  2. ^ Lewis-Beck, Michael (1998): "Series Editor's Introduction", pp. V-vii in: James Jaccard Interaction Effects in Factorial Analysis of Variance , Thousand Oaks, CA: Sage, ISBN 0761912215 ; S. v.

literature

  • GEP Box: Do interactions matter? In: Quality Engineering , Volume 2, 1990, pages 365-369.
  • James Jaccard, Robert Turrisi, Choi K. Wan: Interaction Effects in Multiple Regression . In: Sage University Paper Series on Quantitative Applications in the Social Sciences , No. 72, Newbury Park, Sage 1990.
  • KE Southwood: Nouns Theory and Statistical Interaction: Five Models. In: The American Journal of Sociology , Vol. 83, No. 5, 1978, pages 1154-1203, doi : 10.1086 / 226678 JSTOR 2778190 .