Are you centering your predictor? Making interaction term can lead to large correlation between interaction term and main effect, when yor predictor was not centered.

(If predictor is already centered). Main effect of your IV and interaction effect are overlapping (e.g. correlate). If you enter correlated effects in regression equation simultaneously, both effects will be corrected to each other, and explained variance for IV will decrease. If correlation between your predictor and outcome is relatively small, this decreasing may be critical even you have no collinearity (collinearity is just an extreme case of the same thing). Try to use hierarchical regression and enter interaction after entering main effects.

Hello Eileen,

Your scenario mirrors the classic illustration of a moderator effect. That is, the joint effect (interaction) of IV and moderator are more influential in explaining differences in the outcome variable than either the "main effect" of the IV or the moderator.

See this youtube explanation by Andy Field for more detail and an example:

https://www.youtube.com/watch?v=RqkGMqDU20Q

Good luck with your work!

Hi Eileen,

the presence of a product term changes the interpretation of the effect of both predictor and moderators from unconditional effects ("main effect") to conditional effects ("first-order effects") which represent the effect of the respective predictor for those cases who have a "zero"-value in the moderator (and vice versa). If you've centered predictor and moderator, zero hence is the mean value for the respective variable. In these cases, the first-order effect is the effect of the predictor when the moderator is average.

Here are some must reads for interaction analyses :) The first is more basic and concerns the interpretation issue--the second explains in more detail, how the parameters change (by the way, it destroys the myth that mean centering reduces colinearity) :)

Best,

Holger

Frazier, P. A., Barron, K. E., & Tix, A. P. (2004). Testing moderator and mediator effects in counseling psychology. Journal of Counseling Psychology, 51(1), 115-134.

Echambadi, R., & Hess, J. D. (2007). Mean-centering does not alleviate collinearity problems in moderated multiple regression models. Marketing Science, 26(3), 438-445.

Dear Sirs,

First, I have run predictor and moderator on DV and found that the predictor is significant at p < 0.001 and moderator at p < 0.1. Then, I have added the interaction effect of predictor and moderator. After adding the interactional effect all [predictor, moderator, interaction] become statistically insignificant.

How should I interpret this? Should I say that the moderator neutralizes the significant effect of the predictor on DV?

I found almost the same thing, but my interaction term is significant.

Arnat, please see my post from April, 30th, 2019 that explains that.

All the best,

--Holger

Holger Steinmetz you have mentioned in one of the above comments that "the presence of a product term changes the interpretation of the effect of both predictor and moderators from unconditional effects ("main effect") to conditional effects ("first-order effects")"

While I understand your viewpoint, I am looking for a similar example or an exact reference pertaining to the scenario wherein before introducing moderator, the relationship between independent and dependent variable is insignificant. While upon introducing moderator, the moderation effect is significant between the same independent and dependent variables. This situation is exactly similar to the one asked in following question: (https://www.researchgate.net/post/How_can_we_decide_a_moderation_effect_significant_or_not), where it is argued that moderation makes sense in such a scenario.

I also studied the following paper referred by you:

Frazier, P. A., Barron, K. E., & Tix, A. P. (2004). Testing moderator and mediator effects in counseling psychology. Journal of Counseling Psychology, 51(1), 115-134.

However, the moderation example shared in this paper showcases a scenario wherein direct path between independent and dependent variables is significant while the direct path between moderator and dependent variable is insignificant. At the same time interaction is significantly linked with dependent variable. This is close, but not exactly similar to the situation I am facing.

I am looking for a clear example/reference alluding to the scenario being faced by me. And what is the best way to report such a scenario (i.e. moderation is significant despite non-significant relationship between IV and DV)? Thanks!

Hi,

this paper explains it:

Echambadi, R., & Hess, J. D. (2007). Mean-centering does not alleviate collinearity problems in moderated multiple regression models. Marketing Science, 26(3), 438-445.

Best,

--Holger

Thanks Holger Steinmetz, I studied the paper by Echambadi and Hess (2007). Nowhere they discussed the question/scenario asked by me. Even in table 1 where they share the results of comparison between uncentered and mean-centered approach, the significance of paths hasn't been discussed. If I am missing anything here, please point me towards it.

Harmanjit,

significance vs. non-significance not matters at all. The key is that without a product term, the B_X is the marginal effect of X marginalized across the distribution of Z. In the moment, you include a product term XZ, B_X is the effect of X at one specific location of Z (namely 0). If Z has been centered or standardized before creating the product term, Z=0, hence represents the mean of Z. Therefore, B_X becomes the effect of X for average Z's.

Your scenario seems to be a type of disordinal interaction where the direction of B_X changes from positive to negative, leaving the marginal effect become non-significant. Did you plot the interaction? This would show the point.

Perhaps, the Aiken & West (1991) book would be the next way to go

Aiken, L. S., & West, S. G. (1991). Multiple regression. Newbury Park, CA: Sage.

Unfortunately, I cannot provide anything (e.g., mathematically) more enlightening.

All the best,

--Holger

Hello Atira,

B_X is the regression coefficient (B) for the variable X. The underscore ("_") is often used to signal the indexing of a term. See it as B followed by an X subscripted. XZ is the product term created by multiplying the variables X and Z This product is added in addition to the X and Z variable to show the interaction. If coefficient of the product term (B_XZ) is significant than XZ explains something that is not already contained in X and Z allone (and hence must be the "interaction information") as this goes beyond the linear effects of X and Z.

HTH

Holger

Thanks Holger Steinmetz for your explanation. I am trying to absorb it.

I would appreciate if you can share any research paper, where you have seen situation similar to mine. Thanks again!

Harmanjit Singh unfortunately not. I would suggest searching for "disordinal interaction".

Atira Ety

We speak of moderation when the focus is on X (and Z is regarded as a conditioner) and we use interaction when the focus is on X and Z as causes that multiply in their effects.

Good that you read the Shipley book. It certainly will help even if you use regression. But then, I would dig a bit into econometrics and instrumental variable regression, two-stage least squares, endogeneity.

All the best,

Holger

@Holger Steinmetz, it seems you are right about disordinal interaction in my case. Attached is the plot of interaction. I understand from this that the interaction effect is significant and positive. Is my understanding correct?

This looks strange. This is no disordinal interaction as X has a positive relationship with Y for all levels of M whereas in an disordinal interation the relationship varies from positive to negative.

Based on the plot I would also expect a positive linear effect in a model with out the product term....Further, the interaction is small as the lines vary only a little. Is the product term significant?

Perhaps you can attach a file with the main effects regression model and the model with the product term added.

Best,

Holger

Just to add what was already said: If the interaction term is not included in the regression equation, then the nonlinearity that is actually present - albeit very small - may have the effect of increasing the linear effect somewhat. If the interaction term is now included in the equation, the linear effect is reduced by a small amount, the interaction effect, which is estimated separately.

Is it correct that your linear effect in the linear model is quite small? Then this would be an explanation.

HTH, Karin

Holger Steinmetz, thanks for your feedback. This is alarming for me. Attached are the results as asked by you. Looking forward to your comments.

Additionally, pertaining to your observation that "X has a positive relationship with Y for all levels of M"; I came across following paper (attached herewith); wherein X seems to have positive relationship with Y at all levels of M (Fig. 3 and Fig. 4), yet the moderation effect exists as claimed in this paper.

This is really odd. I am sorry, I have no clue what's going on.....

If you like, you can send me the data (optimally as a csv file). In this case, I need to know details about the variables (what X, M and Y are).

But I understand if you cannot share the data.

Holger

Harmanjit, your problem obviously is different from what I thought, such that you observe non-significant linear effects in the linear model, and in the non-linear model, the linear effects get significant whereas the interaction effect is non-significant.

I think it would be good if you provided more information:

- Are your variables X, M, and Y continuous or categorical?

- Are your variables X, M, and Y normally distributed or skewed?

If they are continuous and both X and M are sort of normally distributed, then you could standardize your variables resulting in X_s, M_s, and Y_s. Then, form the product term X_s*M_s. If you now analyze your two models (linear, nonlinear) using standardized variables, the results may be easier to be compared. In both analyses, the estimates will be standardized estimates.

I am looking forward to your answers.

Kind regards, Karin

Karin Schermelleh-Engel thanks for your comments. Here are answers to your queries:

Well, how large are skewness and kurtosis of the variables? Skewed independent variables pose a problem because artifacts can then occur such that an interaction effect becomes significant even though it is not present in the population, or an interaction effect is not significant even though it is present in the population. However, if skewness is quite small, this should not be a problem. Can you provide some statistics?

Kind regards, Karin

Karin Schermelleh-Engel thanks for your viewpoint.

Here are some statistics:

The kurtosis for 4 items of X variable are as follows: (0.386, 1.167, 1.442, -0.664); for 4 items of M variable are: (0.771, 0.608, 0.586, 0.441); for 3 items of Y variable are: (-0.569, -0.554, -0.537)

Skewness is as follows: For X variable (-1.035, -1.151, -1.242, -0.543); for M variable (-0.931, -0.849, -0.803, -0.697); for Y variable (-0.582, -0.550, -0.568)

Harmanjit, thanks for providing the statistics. As is obvious, all variables are left-skewed, especially the predictor variables, so that a significant moderator effect may be an artifact. Generally, the Y variable should be the only skewed variable. Do you summarize all items pertaining to the same construct? I guess so, because you did not perform a latent moderator analysis. Therefore, the sum scores are also skewed to the left, and the predictor variables are more heavily skewed than the criterion variable.

You could do something more: test the assumptions. Recall that in the linear regression model it is assumed that the errors are independent and follow a normal distribution with constant variance (homoskedasticity). The same is true for the moderator model. I think you should test these assumptions next.

Kind regards,

Karin

Karin Schermelleh-Engel I didn't understand your recommendations exactly. Please explain in exact terms, what exactly I need to do in this case?

Harmanjit Singh, moderated regression has the same assumptions as multiple regression, these should be tested. You can find the assumptions and how to test them in any text book. This link may be helpful:

http://www.sthda.com/english/articles/39-regression-model-diagnostics/161-linear-regression-assumptions-and-diagnostics-in-r-essentials/#regression-assumptions

Kind regards, Karin

Thanks Karin Schermelleh-Engel a lot!

I will read this attachment, and try to apply as per your suggestions.

Hi Eileen Sabbe - curious how your work turned out.

Just wanted to add (because I am not a statistician but I am a research and think about these conceptually) - one commenter made a great point about the moderated effects. It essentially is saying that the main effects you see a relationship but the interaction shows that the third variable is really what is eliciting the effect on the outcome. Essentially, the effect really comes from that third variable. X-> A -> Y. X works through A to get to Y.

Dear Lisa,

you confuse a moderator with a mediator. A moderator does not elicit X's effect but affects its size or direction. That does not preclude that the moderator can ALSO be a mediator. In that case it would elicit part of X's effect and moderate the remaining/direct effect.

All the best

Holger

Holger Steinmetz How would you explain the effects working in this case for this researcher?

Hello Lisa

I already gave a response on April, 30th, 2019 (above).

All the best

Holger