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A follow-up on this unceremoniously deleted question, and before you yet again send me to this one, keep in mind that, as was re-iterated in the original formulation, collinearity is not an issue here (which is the only explanation brought up in that other discussion).

We fit a logistic regression model with about ~10 numerical predictors, for $n=500$ observations (a seemingly respectable sample size) and got the following:

  1. Full model is statistically significant. Here are the ANOVA results using ChiSq test.

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  1. None of the individual predictors are significant in the full model. Here is the model summary.

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  1. No evidence of collinearity (VIF scores all < 2, none of the pairwise correlations are >0.5, etc). Here is the VIF output for the model.

enter image description here

And when enough variables are dropped (e.g. via stepwise selection to reduce the model), the individual predictors eventually start becoming significant.. What might be operating here if not collinearity?

UsDAnDreS
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  • Because *the entire point* of my answer in the duplicate thread was that collinearity is not necessarily an issue, I have to disagree with your premise. You need a better reason to reopen this question. – whuber Jan 22 '21 at 22:20
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    Gotcha, thank you. I've simply responded to your post on there that appeared most relevant, with same question in a more condensed fashion. Situation you describe there appears to still have considerably more evidence of multi-collinearity than in my example (average VIF is about 3.5x what I get). – UsDAnDreS Jan 22 '21 at 22:57
  • Thank you--that's interesting. It would help to have a reproducible example we could experiment with. – whuber Jan 23 '21 at 00:21
  • You don't want to hear it but the issue may still be collinearity - *any* kind of dependence among the $x$-variables, particularly if more than two variables are involved, can explain such a situation. Correlations or VIF don't need to be particularly high; they are not perfect at picking up any possible dependence structure that may explain this. – Christian Hennig Jan 23 '21 at 00:41
  • Another possibility is that all or many variables may have a weak influence, weak enough that it is not picked up by testing them individually, but altogether strong enough to be picked up by the overall model. – Christian Hennig Jan 23 '21 at 00:42

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