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I have fitted a regression model on my mean-centered variables. Every regression coefficient is significantly different from zero but the interaction terms created by multiplying the independent variables together are not.

My queries are:

  1. What could be the possible cause for this weird pattern?
  2. what diagnostics and remedial actions could be taken to correct this?

Update

Actually one of my independent variable in moderator and so the Interaction term that is calculated by multiplying centered-moderator with centered-independent variable should come out as significant but it is not. Now what diagnostic and remedial actions are advised here?

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  • $\begingroup$ what is mean centred variable? Moreover specify your variales incuding dependant variable and output. $\endgroup$ – Subhash C. Davar Apr 11 '16 at 12:55
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    $\begingroup$ @subhashc.davar mean-centered means they subtracted from each variable its average value. The identity of the variables is not relevant to the question. Moreover, 'dependent' has no 'a' and 'variable' contains a 'b' $\endgroup$ – conjugateprior Apr 11 '16 at 13:37
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    $\begingroup$ How do you know that your variable is a moderator? $\endgroup$ – Maarten Buis Apr 11 '16 at 14:01
  • $\begingroup$ domain knowledge $\endgroup$ – Naseer Ahmed Apr 11 '16 at 14:06
  • $\begingroup$ I understand that a moderator is generally a category and multiplying wth a mean centered deviation may cause a problem for computing interaction. better to look for a probability estimate to reach at at interactiob. $\endgroup$ – Subhash C. Davar Apr 11 '16 at 14:59
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There is nothing necessarily weird about this pattern and there may be no remedial actions to be taken.

Many models don't have important or significant interactions. This could be one of them. Since you don't give any context, we have no way to even guess.

But it also could be any of a number of things, e.g.:

  • If the variables are measured with error, the interaction has more error, so it's harder to be significant.

    The sample size and power could be small.

    The interaction might not be well captured by multiplying the two variables.

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  • $\begingroup$ Actually one of my independent variable is moderator variable and presence and absence of that term should be significant so it means that my (moderator).(Independent variable) Interaction term should come out as significant but it is not.What remedial measures are necessary now so that my moderator has significant interaction with Independent variable? $\endgroup$ – Naseer Ahmed Apr 11 '16 at 13:42
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    $\begingroup$ The fact that you believe that a variable is a moderator does not mean that the data has to agree. Whether or not you call a variable a moderator is a theory and theories can be (and often are) wrong. Having said that, all the altervative reasons that Peter suggested are possible to. Without all the details we cannot tell. $\endgroup$ – Maarten Buis Apr 11 '16 at 14:00
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    $\begingroup$ If you want a better answer, you have to ask a better question. My blog post how to ask a statistics question may help $\endgroup$ – Peter Flom - Reinstate Monica Apr 11 '16 at 14:02
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My immediate thoughts are that you're using both the interactions and the existing variables in the same model. In this case, it may be that their interactions are insignificant as the value is captured in the individual variables. This may not be an issue/mistake with your model and instead with your line of thinking.

If you wish to test this (see comments below why this isn't a good idea), omit one (or two) of the variables, and leave the interaction terms in. I am not saying that doing so is best practice or recommended, but you will probably see this interaction become significant.

Is there any reason why you would want an interaction, or why one is desired?

In summary,

  1. There is no significant interaction effect between variables or all the value is captured by the individual variables.

  2. This is not necessarily an issue that needs correcting.

Note: This should be a comment, but unfortunately, I don't have the required reputation.

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  • $\begingroup$ Are you suggesting to remove the main effects while keeping the interaction effects in the model? $\endgroup$ – Maarten Buis Apr 11 '16 at 12:38
  • $\begingroup$ I'm suggesting that doing so would probably lead to the interaction being significant. I'm not advising or recommending that doing so is best practice or would lead to a better answer. $\endgroup$ – Matt Triggs Apr 11 '16 at 12:39
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    $\begingroup$ Ok, I think we can agree that technically it is an answer: but in practice one should not do that. I wonder if this answer helps or causes more confusion. $\endgroup$ – Maarten Buis Apr 11 '16 at 12:44
  • $\begingroup$ I agree. I would've put this as a comment, but as mentioned, I don't have the required reputation. I will clarify my answer. $\endgroup$ – Matt Triggs Apr 11 '16 at 12:50
  • $\begingroup$ Echoing @MaartenBuis, please don't suggest leaving lower order effects out to someone who is not yet clear on how interactions work to start with. $\endgroup$ – conjugateprior Apr 11 '16 at 13:42

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