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Moderating (Interaction) Effects in Regression
Chuck Huber, PhDStataCorp
University of California RiversideNovember 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
Outline
• What is moderation (interaction)?
• Binary moderators
• Testing for interaction
– F-tests
– Likelihood ratio tests
• Categorical moderators
• Continuous moderators
• Multiple Moderators
Outline
• What is moderation (interaction)?
• Binary moderators
• Testing for interaction
– F-tests
– Likelihood ratio tests
• Categorical moderators
• Continuous moderators
• Multiple Moderators
Outline
• What is moderation (interaction)?
• Binary moderators
• Testing for interaction
– F-tests
– Likelihood ratio tests
• Categorical moderators
• Continuous moderators
• Multiple Moderators
Outline
• What is moderation (interaction)?
• Binary moderators
• Testing for interaction
– F-tests
– Likelihood ratio tests
• Categorical moderators
• Continuous moderators
• Multiple Moderators
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))
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