I am given a binary logistic regression data set with 3 predictor variables:

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I am asked Do you think a simpler model would be preferable? Explain. My answer is Yes because the variable cell is not statistically significant, but I read online that if a regression model has variables that are correlated it must be removed. Can someone please explain?

  • $\begingroup$ Can you provide a link to your online source? $\endgroup$ – AdamO Nov 6 '17 at 21:47
  • $\begingroup$ analyticbridge.datasciencecentral.com/group/… $\endgroup$ – leems Nov 6 '17 at 21:48
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    $\begingroup$ This is a vague question: in what sense does it mean "preferable"? Regardless, for many reasonable meaning of the word (such as prediction accuracy, estimation of coefficients, or appropriateness to subject matter), there is not enough information here to determine an answer. Moreover, these statistics provide no information at all about correlations among the independent variables, so they won't serve to address the last question, either. The site you link to does not seem to contain any further information about this software output. $\endgroup$ – whuber Nov 6 '17 at 22:18
  • $\begingroup$ I am not exactly sure. I assumed it to be prediction accuracy. Ilooked at the OR , CI and p-value and based on those answars came up with the conclusion of statistical significance, not sure if that's enough. And thank you, I understand why the statement would not apply to this case. $\endgroup$ – leems Nov 6 '17 at 22:30
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    $\begingroup$ @leems the problem is that model coefficients have nothing to do with predictive accuracy, making the whole question a red herring. $\endgroup$ – AdamO Nov 6 '17 at 22:35

You should not base your choice of model on the statistical findings from candidate models. Doing so is considered statistical fishing. Covariates should be specified in a model a priori based on a deep understanding of a scientific question and the study design. Variables should be included in a logistic model if they are confounding variables, prognostic variables, blocking factors, or main effects for interactions. Adding or removing factors from a logistic model changes the estimation and interpretation of the coefficients.

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    $\begingroup$ From what I understand, the variable cell is not prognostic or confounding variable. Should it still be included? or in what case do we exclude variables? $\endgroup$ – leems Nov 6 '17 at 22:07
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    $\begingroup$ Resist the temptation to remove insignificant variables. This ruins the model's standard errors. $\endgroup$ – Frank Harrell Nov 6 '17 at 23:13
  • $\begingroup$ You'd need to use a model comparison approach - full vs reduced, to know for sure. You can't know based only on the p values. $\endgroup$ – HEITZ Nov 6 '17 at 23:51

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