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I have a logistic model where I modeled an independent variable at both first order only and then as a second order polynomial (via the poly function in R). I noticed that the p-value for the IV decreased significantly from 10^-4 to 10^-77. However, when I look at the summary output for both first and second order terms, the first order appears to not be statistically significant (high Pr(>|z|)).

             Pr(>|z|)

poly(log(x), 2)1 0.420098
poly(log(x), 2)2 0.000322 ***

Does this mean that the first order term should be removed from the model, and if so what is the syntax to do so?

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    $\begingroup$ Not sure to understand the question. "Greater stat significance" is not something relevant. The meaning of the quadratic term is not the same at all depending on whether or not you include the 1st order term in the model. $\endgroup$ – Umka Jun 6 '17 at 20:46
  • $\begingroup$ not sure I understand the question. $\endgroup$ – Haitao Du Jun 7 '17 at 17:12
  • $\begingroup$ @hxd1011 - reworded for hopefully better clarity $\endgroup$ – Frank H. Jun 7 '17 at 17:28
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Lack of statistical significance is never a sufficient reason to remove a predictor from a regression model. So the answer to your question is simply, no.

Does it matter that I would leave in the second order term versus? That is, I would not remove the entire variable - both first and second order terms?

If you remove the first order term from the model, you are telling the model that you are 100% confident that the rate of change of y with respect to log(x) is zero at the origin. Are you 100% confident of this?

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  • $\begingroup$ Does it matter that I would leave in the second order term versus? That is, I would not remove the entire variable - both first and second order terms. $\endgroup$ – Frank H. Jun 7 '17 at 17:43
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    $\begingroup$ If you remove the first order term from the model, you are telling the model that you are 100% confident that the rate of change of y with respect to log(x) is zero at the origin. Are you 100% confident of this? $\endgroup$ – Matthew Drury Jun 7 '17 at 17:44
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    $\begingroup$ Why not edit your comment into the answer Matthew as it goes to the heart of the matter. $\endgroup$ – mdewey Jun 7 '17 at 17:46
  • $\begingroup$ @mdewey It is done! $\endgroup$ – Matthew Drury Jun 7 '17 at 17:47
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    $\begingroup$ Removing the first order terms changes the meaning of the second order term. It no longer reflects what you think it reflects. $\endgroup$ – dbwilson Jun 7 '17 at 17:49

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