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What if interaction wipes out my direct effects in regression?

I have three hypotheses within my experiment, and interpreting the interaction in relation to the rest of the results is what I am having difficulty with.

  1. The first is that the IV in the model (with two levels) will be related to one DV but not the other (time 1, but not time 2).

    A repeated measures GLM indicated that the IV was related to the both DVs.

  2. The second hypothesis was that a covariate will be related to one DV and not the other.

    Using a repeated measures GLM this hypothesis was supported.

  3. Predicted an interaction between the IV, DV and a covariate. (A repeated measures GLM with IV (fixed factor), DVs (within factor), covariate).

What I found was no effect of the covariate, no effect of the interaction, however my main effect for IV and DVs was gone (p=0.075) (hypothesis one).

Now I know p=0.05 isn't everything, so I have two questions.

How would I go about interpreting the fact that my main effect for hypothesis one disappeared IF:

  1. you don't consider p=0.05 a black and white cut off point?
  2. you do consider p=0.05 a black and white cut off point?

Does it change how I interpret the results from hypothesis one, or their meaning? Does it make it redundant?

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Rebecca Anderson
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  • I notice you used the *generalized-linear-model* tag, but you don't say much about the nature of your DV. Is is binary? Or did you mean the [general linear model](http://en.wikipedia.org/wiki/General_linear_model)? – gung - Reinstate Monica Sep 27 '12 at 22:20
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    This seems to be a very common question. You may also want to look at these related Q's on CV: [what-if-interaction-wipes-out-my-direct-effects-in-regression?](http://stats.stackexchange.com/questions/5450/); [interaction-suppresses-the-main-effect-how-to-interpret-it](http://stats.stackexchange.com/questions/16178/); & this is also related (albeit from the other direction): [how-to-interpret-inconsistent-beta-values-in-different-steps-of-hierarchical-reg](http://stats.stackexchange.com/questions/32653/). – gung - Reinstate Monica Sep 27 '12 at 22:40
  • yes i already looked at two of those answers. No sorry thats a mistake, i meant the general linear model... – Rebecca Anderson Sep 28 '12 at 00:06
  • No problem, @Rebecca-Anderson, that's one of the issues w/ those; the names are practically identical & easy to confuse. Re the other answers, it might help if you could state what you learned towards answering your questions there, & what wasn't covered / you still don't understand. – gung - Reinstate Monica Sep 28 '12 at 00:13

1 Answers1

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First off, you didn't (I am sure) find "no effect" in any case for any effect; you found no significant effect. The key thing to look at is the effect size (parameter estimate), with and without the interaction, and see how it changes.

Second, certainly adding an interaction can change a main effect - it can make it larger or smaller. When you have an interaction in the model, say $X_1*X_2$, then the main effect for $X_1$ is the effect of change in $X_1$ when $X_2 = 0$ (similarly, the main effect for $X_2$ is the effect of change in $X_2$ when $X_1 = 0$).

Since your IV has 2 levels, let's use (as an example) that it is sex, coded 0 for male and 1 for female. Then the effect of the covariate when the interaction is in the model is the effect of the covariate for males. If it is smaller then the main effect of the covariate without the interaction, that means the effect of the covariate is smaller for males than for females.

Peter Flom
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  • If the interaction is not significant, do i interpret the main effects from a model without the covariate (so with a fixed factor/IV with two levels (hot and cold) and the within factor DVs), or the interaction model (Fixed/within/covariate)? – Rebecca Anderson Sep 27 '12 at 11:11
  • If the interaction is not significant it simply means that, if, in the population from which the sample was drawn the effect there was no difference in the effect for men and women (e.g) then there is a $> 0.05$ chance of getting an interaction term as large as the one you got or larger. Depending on N, large effects can be nonsignificant and small effects can be significant. – Peter Flom Sep 27 '12 at 11:14
  • Thankyou. But how do i interpret main effects? Do i look at another model with the IV and DV but no covariate. Or do i look at the main effects in the context of the model with the interaction? – Rebecca Anderson Sep 27 '12 at 12:13
  • It depends on what you want to do. For the first two hypotheses it looks like you want just main effects; for the third you need to include an interaction term. – Peter Flom Sep 27 '12 at 13:09
  • ah ok. but in light of the 3rd hypothesis doesn't that make the 1st hypothesis redundant? so even though what i hypothesised was confirmed, i cant meaningfully (as in real world implications) interpret that the IV had an effect on the DVs, as in light of the third hypothesis adding a covariate in the model reduces the effect of this IV-DVs relationship to non-significance? – Rebecca Anderson Sep 27 '12 at 13:19
  • Statistically, it's meaningful. Whether it is substantively meaningful is another matter. Usually, if there is an interaction, the main effects models without interaction are not good. Some people decide based on whether the interaction is statistically significant. I think this is an error. It is better to look at the effect size of the interaction and its effects on the other effect sizes. However, in the social sciences anyway, you may have trouble "selling" my view. – Peter Flom Sep 27 '12 at 13:30