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Thread: What is the difference between an interaction effect and a moderator in regression?

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    What is the difference between an interaction effect and a moderator in regression?




    I hear these two concepts a lot in the literature. I have no idea what the difference is between a moderator and an interaction term.

    While I am at it, mean centering predictor variables is often recommended when dealing with interaction. I am not sure how you handle categorical variables this way, do you mean center them - I would not think so. Also I assume you only mean center the main effects not interaction terms.
    Last edited by noetsi; 01-28-2016 at 02:19 PM.
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    Re: What is the difference between an interaction effect and a moderator in regressio

    These terms are synonyms most all of the time. You just need to think about the causal graph, where in mediation the terms are aligned and in moderation there is typically a T were X connects to Y and perpendicular line is the effect of X2 on the effect of X1 on Y.


    No centering when dealing with categorical variables.
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    Re: What is the difference between an interaction effect and a moderator in regressio

    So when you have some interval and some categorical variables can you change the interval variables and leave the categorical ones the way they were? I can't think of any reason you can't....
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: What is the difference between an interaction effect and a moderator in regressio

    You don't need to do anything. I refer to Jakes post where he covered centering and collinearity. I believe that is what's going on here. But this would not be an issue with categorical or categorical*ordinal.
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    Re: What is the difference between an interaction effect and a moderator in regressio

    What I meant is if centering interval variables would change the interpretation of categorical variables in some way that is invalid. But I realize now it won't.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: What is the difference between an interaction effect and a moderator in regressio

    Remember there are two forms of centering when it comes to interaction/moderation - grand mean centring or group mean centring.
    There are various extensive arguments surrounding both within literature.

    It also depends on the type of analysis you are doing. Centring is typically used to aid interpretation, but it can also eliminate variation.

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    Re: What is the difference between an interaction effect and a moderator in regressio

    I had not heard that it reduces variation although it eliminates multicolinearity. The centering I do is centered at the mean of each predictor.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: What is the difference between an interaction effect and a moderator in regressio

    Nice blog by Andrew Gelman on the pros and cons of centering. http://andrewgelman.com/2009/07/11/when_to_standar/

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    Re: What is the difference between an interaction effect and a moderator in regressio

    Miner I found that article really interesting, but in honesty it seemed to be about reporting data in terms of raw scale or standard deviations (betas) not centering.

    I suspect I missed something....
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: What is the difference between an interaction effect and a moderator in regressio

    One thing I notice about MC is that while it is said never to bias a model parameter just the SE this is really not true in practice in many cases. When you add a variable to a model with high MC it can significantly change the slope or sign of another variable that was in the model. While this is true, I believe, generally in multivariate regression the results seem more extreme when MC is involved.

    Or maybe not I am not sure of this.
    Last edited by noetsi; 02-01-2016 at 09:59 AM.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: What is the difference between an interaction effect and a moderator in regressio

    To muddy the waters even more, you have two variables that are collinear and you can also have mediators. Mediators can effect estimates quite a bit and are obviously collinear, since they are endogenous (antecedents).
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    Re: What is the difference between an interaction effect and a moderator in regressio

    Joy By mediators you mean interaction terms, right?
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: What is the difference between an interaction effect and a moderator in regressio

    Nope. A completely different beast.
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    Re: What is the difference between an interaction effect and a moderator in regressio

    The only term if know that involves mediation are intervening variables in SEM models.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: What is the difference between an interaction effect and a moderator in regressio


    I have been reviewing my old class notes and I noticed something. It appears for linear regression that when two variables interact and one of these is a dummy variable, than the interaction slope is the difference between the interval [non-dummy] variable slope at the two levels of the dummy variable. So if B1 is the slope of the dummy, B2 the slope of the interval variable and B1B2 =.5 the slope of B2 will be .5 different at the two levels of the dummy variable.

    When the slope of the interaction term is negative the slope of the interval main effect will be .5 higher when the dummy takes on the value 0. And when the slope of the interaction term is positive than the interval main effect will be .5 higher when the dummy takes on the value 1.

    Or are my class notes wrong
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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