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So, I have this dataset with a hormonal measure as independent variable and behavioral measures as dependent variables. I am using a linear regression as my model and after a backward selection, ended up with 4 significant dependent variables. However, I forget to include in it the age and sex of individuals. So my question is, in order to include them in the model and keep them for control, can I procede to my backward elimination by ignoring these 2 variables and keeping them in there despite their p-values of 0.7-0.8? Or I should simply remove them when they become the least significant vars?

Is there also any other way to control for two variables without using them as dependent variables?

Thank you! Jessica

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    $\begingroup$ What gave you the idea that removing "insignificant" variables is a good idea? This invalidates almost every aspect of statistical inference. $\endgroup$
    – Frank Harrell
    Jul 13, 2015 at 16:53

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You should not do backward elimination at all. Nor forward. Nor stepwise. Not only does using any of these make all of your results incorrect, it also stops you from thinking.

There are many reasons to include variables in a model. You have identified one of them: As control variables. So, include age and sex.

Then include any other variables that are substantively important. A small effect where a large one is expected is sometimes more interesting than a large one where a small one is expected.

You should also include variables if they affect other parameters in the model.

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    $\begingroup$ Hi Peter, I must say that I agree with your view on those kind of model selection, it does feel like shopping for a model. However, how does one define what is a substantively important variable? I mean, I have reviewed a bunch of literature prior to the analysis and I included only the ones that were highlighted as relevant. I guess it's only a judgement call tho Also, I have a hard time to determine whether I should include variables interactions or not, as I did not find any article pointing toward those, but it seems highly unlikely to me that no behavioral data interacts (next comment) $\endgroup$
    – user82189
    Jul 13, 2015 at 17:44
  • $\begingroup$ with sex or age (this one being a dummy, young/old). Is there a way to get hints of an interaction by making a matrix of some correlation etc? (I know correlation =/= interaction my teacher's been clear enough) Also, can it be problematic to have various types of independant variables (probability 0 to 1, dummy 0 or 1, time 0 to 60 sec)? Oh and just a last one if you got time, if in the big un-modified model age and sex got high p-values (.6x), is there something to discuss about them or solely say they are in there for control? Thank you so much for the clarifications! Jess $\endgroup$
    – user82189
    Jul 13, 2015 at 17:49
  • $\begingroup$ Yes, it's a judgement call. That's part of being a researcher - making expert judgements. As to interactions, you can just multiply the two terms. However, using age as just young/old is a mistake if you can get actual. age. $\endgroup$
    – Peter Flom
    Jul 14, 2015 at 19:32
  • $\begingroup$ Thanks again. Sure is a flaw in the data, tho it is the only one I have with this dataset. Cheers :) $\endgroup$
    – user82189
    Jul 14, 2015 at 20:34

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