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I am using multiple regression with the backward elimination method. I have one control variable (social desirable responding) and four predictor variables (gender and three self-esteem constructs). My dependent variable is risky sexual behavior. I entered social desirable responding in the first block and selected "backward" as the method. I entered the four predictor variables in the second block and selected "backward" as the method.

My questions are:

Am I supposed to examine the results with the just the main effects, determine the IVs that are significant, and run a separate analysis with interaction terms that contain only significant IVs?

If so, should I run the analysis again with all of the main effects in one block and the interaction terms with the significant IVs in another block?

Or should I not run separate analyses for the main effects and interactions, and instead just run them all at one time but in separate blocks?

Thanks so much

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It is not a good idea to use stepwise regression for reasons detailed multiple times on this site. It is also not a good idea to use statistical significance for formulating the model. Rather use subject matter knowledge. Also respect the hierarchy principle whereby main effects are always included for terms in which interaction is allowed.

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  • $\begingroup$ A link to a CV answer or wiki that nicely enumerates these important points would give a nice polish to your answer (if not actually enumerating them here). :) $\endgroup$
    – Alexis
    Aug 19, 2014 at 14:34
  • $\begingroup$ @Frank, I've also read about including main effects for terms in which interaction is allowed in the book ISLR. But recently came across some example, where model improves (as suggested by adjusted R2, AIC, BIC), if I exclude main effects and keep only interaction term. Also sometimes including main effects make some other predictor insignificant. Can you please share your views on this issue. $\endgroup$
    – Dr Nisha Arora
    Jun 6, 2016 at 12:21
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    $\begingroup$ All these issues have been discussed in great detail on this site. To answer the question about interactions without main effects, this is a violation of the hierarchy principle in statistical modeling, which causes major damage, e.g., being highly sensitive to the scale origin for variables and being hard to interpret. $\endgroup$
    – Frank Harrell
    Jun 6, 2016 at 12:39

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