Editing Interaction (statistics) (section)

===In regression===

The most general approach to modeling interaction effects involves regression, starting from the elementary version given above:

:<math>Y = c + ax_1 + bx_2 + d(x_1\times x_2) + \text{error} \,</math>

where the interaction term <math>(x_1\times x_2)</math> could be formed explicitly by multiplying two (or more) variables, or implicitly using factorial notation in modern statistical packages such as [[Stata]]. The components ''x''<sub>1</sub> and ''x''<sub>2</sub> might be measurements or {0,1} [[dummy variable (statistics)|dummy variable]]s in any combination. Interactions involving a dummy variable multiplied by a measurement variable are termed ''slope dummy variables'',<ref>Hamilton, L.C. 1992. ''Regression with Graphics: A Second Course in Applied Statistics''. Pacific Grove, CA: Brooks/Cole.  {{ISBN|978-0534159009}}</ref> because they estimate and test the difference in slopes between groups 0 and 1.

When measurement variables are employed in interactions, it is often desirable to work with centered versions, where the variable's mean (or some other reasonably central value) is set as zero. Centering can make the main effects in interaction models more interpretable, as it reduces the [[multicollinearity]] between the interaction term and the main effects.<ref>{{Cite journal|last1=Iacobucci|first1=Dawn|last2=Schneider|first2=Matthew J.|last3=Popovich|first3=Deidre L.|last4=Bakamitsos|first4=Georgios A.|date=2016|title=Mean centering helps alleviate "micro" but not "macro" multicollinearity|journal=Behavior Research Methods|language=en|volume=48|issue=4|pages=1308–1317|doi=10.3758/s13428-015-0624-x|pmid=26148824 |issn=1554-3528|doi-access=free}}</ref> The coefficient ''a'' in the equation above, for example, represents the effect of ''x''<sub>1</sub> when ''x''<sub>2</sub> equals zero.

[[File:Tea party interaction.png|thumb|Interaction of education and political party affecting beliefs about climate change]]Regression approaches to interaction modeling are very general because they can accommodate additional predictors, and many alternative specifications or estimation strategies beyond [[ordinary least squares]]. [[Robust regression|Robust]], [[Quantile regression|quantile]], and mixed-effects ([[Multilevel model|multilevel]]) models are among the possibilities, as is [[generalized linear model]]ing encompassing a wide range of categorical, ordered, counted or otherwise limited dependent variables. The graph depicts an education*politics interaction, from a probability-weighted [[logit regression]] analysis of survey data.<ref>{{cite journal | last1 = Hamilton | first1 = L.C. | last2 = Saito | first2 = K. | year = 2015 | title = A four-party view of U.S. environmental concern | journal = Environmental Politics | volume = 24 | issue = 2| pages = 212–227 | doi = 10.1080/09644016.2014.976485 | bibcode = 2015EnvPo..24..212H | s2cid = 154762226 }}</ref>