0
$\begingroup$

One assumption of running a logistic regression is that the continuous predictors are linearly related with the log odds.

However, wouldn't it technically be better if it was shaped as is the logit function below, not really linear? I understand that the logit function is roughly linear when probabilities are between .3 and .7, but what about for very high or low probabilities where you test your assumption and it might not look, strictly speaking, linear?

enter image description here

Improve this question
$\endgroup$
4
  • $\begingroup$ It would be that S-shape for the probability, not the log-odds. $\endgroup$
    – Dave
    Jan 20, 2021 at 21:04
  • $\begingroup$ sorry, not quite "S" I suppose, I will rephrase and edit $\endgroup$
    – biostatguy12
    Jan 20, 2021 at 21:08
  • 2
    $\begingroup$ It isn’t a generalized linear model because a line fits that curve in the middle of the curve. It’s a generalized linear model because it posits that the log-odds literally follows a linear pattern. (But then the probability does not!) $\endgroup$
    – Dave
    Jan 20, 2021 at 21:45
  • 1
    $\begingroup$ gotcha! Really helpful, thanks $\endgroup$
    – biostatguy12
    Jan 20, 2021 at 21:46

1 Answer 1

Reset to default
0
$\begingroup$

Partially answered in comments:

It isn’t a generalized linear model because a line fits that curve in the middle of the curve. It’s a generalized linear model because it posits that the log-odds literally follows a linear pattern. (But then the probability does not!)

– Dave

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.