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Thread: non-significant predictor became significant after including additional predictor?

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    non-significant predictor became significant after including additional predictor?




    Hi everyone, I have a quick question concerning a program I am having in multiple regression.

    I have a working full mediation model, that is, after including the mediator, my significant independent variable x1 became non-significant.

    However, after adding another variable (x2) in to the multiple regression (y, x1, mediator, x2), x1 became significant again, even when the mediator is present (and significant as well). x2 is also significant.

    What kind of problems am I looking at? I apologize ahead of time if this has been asked and answered before.

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    Re: non-significant predictor became significant after including additional predictor

    Assuming that (y, x1, mediator, x2) is the true model you have omitted variable problem when estimating the model (y, x1, mediator) which very plausible creates bias see wiki on: Omitted-variable_bias and makes the OLS estimator inconsistent. This bias and inconsistency is one argument for not starting with a minimal model and adding variables but instead starting from af maximal model - including all variables, interaction etc. - and then reducing.... since the OLS estimator will still be consistent if you estimate a model including variables not included in the true model.

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    Re: non-significant predictor became significant after including additional predictor

    Thanks so much!

    I have two more questions.

    1. What effects (or mechanisms) from x2 might cause x1 to become significant again even in the presence of the mediator?

    2. Would my description of the mediation model be something like "when controlling for x2, the mediation model no longer hold true"?

    Or would it be something like "x1 holds unique predicting power after controlling for x2"?

    I am sorry for asking questions like this, but statistics is really not something I do a lot...

    Thanks again!

    David

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    Re: non-significant predictor became significant after including additional predictor

    1. What effects (or mechanisms) from x2 might cause x1 to become significant again even in the presence of the mediator?
    "significant/non-significant" are quite poor descriptions,
    given that this could mean 0.049 versus 0.050 as well
    as 0.00001 versus 0.90 . In addition, it is always useful
    to mention sample size.

    Regarding your question, maybe this is some kind
    of -> suppressor effect.

    With kind regards

    K.

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    Re: non-significant predictor became significant after including additional predictor

    This is an example of why one should work from some theory when running statistics if possible. To know what mechanism in X2 might cause X to behave in such a way you need to have a theory, either your own or other authors, which you can then test. Trying to decide this empirically is extremely difficult (that is trying to decide it purely based on the data without substantive knowledge of what you are analyzing).
    "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: non-significant predictor became significant after including additional predictor

    Thanks, sample size is 120. and below is the SPSS output table.

    Last edited by jiaxiking; 01-05-2015 at 02:42 PM.

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    Re: non-significant predictor became significant after including additional predictor

    Quote Originally Posted by noetsi View Post
    This is an example of why one should work from some theory when running statistics if possible. To know what mechanism in X2 might cause X to behave in such a way you need to have a theory, either your own or other authors, which you can then test. Trying to decide this empirically is extremely difficult (that is trying to decide it purely based on the data without substantive knowledge of what you are analyzing).
    Sorry about the confusion. As a novice in stats, I am trying to figure out the mechanisms of what I'm doing. There are theories behind the mediation model and x2 is closely related to the other variables (like control).

    I guess what I'm trying to say is, is what I experienced something like "by controlling for x2, the mediation effect became insignificant"?

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    Re: non-significant predictor became significant after including additional predictor

    I was addressing this question:

    What effects (or mechanisms) from x2 might cause x1 to become significant again even in the presence of the mediator?
    My point was that this is not really a statistical question. The answer is almost certainly substantive, that is in the phenomenon itself not the way your model runs. Or rather the model produced what it does because of something in the substance.

    A simple example of this is that in regression you control for something methodologically by only considering the unique impact of a variable. But the reason that this matters, that there is overlap in explained variation in the first place is because substantively two or more predictors are explaining the same variation.
    "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: non-significant predictor became significant after including additional predictor

    Thanks again, and sorry for all the trouble.

    I tried to google for answers but most search results are on "when including additional variable, significant predictors became insignificant". I can understand that without any problem.

    I wonder would it be possible if you could provide a template of explanation like "x2 suppressed the mediator" or something like that without referring to the actual meanings behind the variables?

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    Re: non-significant predictor became significant after including additional predictor

    I am, unfortunately, not the one to help with that. I do not work with mediation effects enough to provide it. One thing to be careful about is that aside from mediation effects [which again I can't comment on] another statistical effect that can cause a variable to become non-signficant when you add another variable is multicolinearity [this is totally different than mediation]. So to rule that, multcollinearity, out you might run a VIF or tolerance test.
    "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: non-significant predictor became significant after including additional predictor


    Thanks again. Isn't the difference between multicolinearity and mediation that a mediation model would require logical (or theoretical) explanations behind the variable relationships?

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