Moderating (Interaction) Effects in Regression Chuck Huber, PhD StataCorp chuber@stata.com University of California Riverside November 14, 2016
Outline What is moderation (interaction)? Binary moderators Testing for interaction F-tests Likelihood ratio tests Categorical moderators Continuous moderators Multiple Moderators
What is Moderation? A moderator is a variable that affects the direction and/or strength of a relationship between an independent or predictor variable and a dependent or criterion variable. (Baron & Kenny, 1986, pg 1174). Moderation (or interaction) occurs when the strength or direction of the effect of a predictor variable on an outcome variable varies as a function of the values of another variable, called a moderator. (Marsh et al, 2013, pg 361).
What is Moderation? M X Y The effect of X on some variable Y is moderated by M if its size, sign, or strength depends on or can be predicted by M. In that case, M is said to be a moderator of X s effect on Y, predicted by M. (Hayes, 2013, pg 208).
Example: Age (X), SBP (Y) and Sex (M) The effect of age (X) on SBP (Y) is not the same for males and females. Thus sex is a moderator for the relationship between age and SBP.
Example: Age (X), SBP (Y) and Race (M) The effect of age (X) on SBP (Y) is not the same for all categories of race. Thus race is a moderator for the relationship between age and SBP.
Example: Age (X), SBP (Y) and HDL (M) The effect of age (X) on SBP (Y) is not the same for all levels of high-density lipoprotein (HDL). Thus HDL is a moderator for the relationship between age and SBP.
Outline What is moderation (interaction)? Binary moderators Testing for interaction F-tests Likelihood ratio tests Categorical moderators Continuous moderators Multiple Moderators
Regression for SBP and Age
Margins for Age
marginsplot Marginsplot for Age
Regression for Age (X) and Sex (M)
Regression for Age (X) and Sex (M)
Margins for Age (X) and Sex (M)
Marginsplot for Age (X) and Sex (M) marginsplot
Outline What is moderation (interaction)? Binary moderators Testing for interaction F-tests Likelihood ratio tests Categorical moderators Continuous moderators Multiple Moderators
F-test for Interaction
F-test for Interaction
Likelihood Ratio Test for Interaction
Likelihood Ratio Test for Interaction
Likelihood Ratio Test for Interaction
Outline What is moderation (interaction)? Binary moderators Testing for interaction F-tests Likelihood ratio tests Categorical moderators Continuous moderators Multiple Moderators
Regression for Age (X) and Race (M)
Margins for Age (X) and Race (M)
Marginsplot for Age (X) and Race (M) marginsplot, recast(line) noci
F-Test for Interaction Tests for Interaction Likelihood Ratio Test for Interaction
Outline What is moderation (interaction)? Binary moderators Testing for interaction F-tests Likelihood ratio tests Categorical moderators Continuous moderators Multiple Moderators
Regression for Age (X) and HDL (M)
Margins for Age (X) and HDL (M)
Contour Plot for Age (X) and HDL (M)
F-Test for Interaction Tests for Interaction Likelihood Ratio Test for Interaction
Outline What is moderation (interaction)? Binary moderators Testing for interaction F-tests Likelihood ratio tests Categorical moderators Continuous moderators Multiple Moderators
Regression for Age (X), Sex (M1) and Race (M2)
Marginsplot for Age (X), Sex (M1) and Race (M2) margins sex#race, at(age=(20(10)60)) vsquish marginsplot, recast(line) noci legend(rows(2))
F-Test for Interaction Tests for Interaction Likelihood Ratio Test for Interaction
References 1. Baron, RM & Kenny, DA. (1986) The Moderator-Mediator Variable Distinction in Social Psychological Research: Conceptual, Strategic, and Statistical Considerations. Journal of Personality and Social Psychology. Vol. 51, No. 6, 1173-1182 2. Hayes, AF. (2013). Introduction to Mediation, Moderation, and Conditional Process Analysis. Guilford: New York 3. Herbert WM, Hau KT, Wen Z, Nagengast B,& Morin AJS (2013). Moderation. In Little TD (editor), The Oxford Handbook of Quantitative Methods, Volume 2 (pp 361-386). Oxford: Oxford