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I have a question (simpler than my previous post today I hope!), which is probably very stupid as nobody has never asked it before.

Lets say I am trying to explain the effect of 3 variables (A, B and C) on a dependent one (Y). Biologically speaking, A and B should really have an effect on Y. So I am testing:

Y ~ A + B + C

But when I use a model selection method (whatever the method is), the 'best' model, the one that fits the data the best, drops A. So I end up with:

Y ~ B + C

What can I say about A then?

Can I cite something to justify the dropping (the F statistics, something about the AIC/BIC, etc)?

OR

If I need to show that A has no effect, do I need to use the full model anyway?

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  • $\begingroup$ AIC, BIC, DIC, Likelihood Ratio, cross-validation, etc... are tools that you can use depending on the features of the model you are interested on. If they indicate that A can be dropped, then you could use the Occam's razor to defend the model $B+C$. The other post is interestig, but a bit long. Shorter questions seem to be more successful, you know, the popular TL;DR. $\endgroup$ – user10525 May 1 '12 at 19:57
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    $\begingroup$ Thanks. And I agree for the tl;dr thing, but I like to be clear, and thats also a very specific case, so I had to fully describe it. Thats the complexity of that dataset that makes it challenging to analyze. $\endgroup$ – Joe May 1 '12 at 20:47
  • $\begingroup$ And for your answer here: it's not really my question though=> I want to know what to say about the dropped variable. I need a way to prove that it had no effect. $\endgroup$ – Joe May 1 '12 at 20:49
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    $\begingroup$ Don't confuse dropping a variable with having no effect, Joe! For example, let y ~ a+d+e, b=a/2+2d+e/2, c=a/2-d+e/2, with d, e, (and the implicit error) all small compared to the variation in a. Then a may have a profound effect on y, but (due to its association with b and c) is unnecessary in the model (and won't even be significant in the full model y ~ a+b+c); the best model would be y ~ b+c (because this equals a+d+e). $\endgroup$ – whuber May 1 '12 at 21:13
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    $\begingroup$ @whuber That's very well-put. Why not make it an answer? $\endgroup$ – Matt Parker May 1 '12 at 22:28
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It depends on your aim. Since A "really should" have an effect on Y but appears not to, I would definitely include the full model. As Procrastinator suggests, model selection might be useful to propose a parsimonious new model - if that's your objective. But if your objective is to estimate the relationships between your predictors and Y, then I don't think you need a model selection step at all - just present your full model results.

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  • $\begingroup$ Ok thanks. I guess I got confused about the role of model selection, which is probably not appropriate in that case. I just thought that 'fitting the data better' was better, but actually it's not here! $\endgroup$ – Joe May 1 '12 at 21:33

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