I was trying to fit logistic regression with a binary response variable and a continuous predictor variable. But when I plotted the fitted probabilities vs the predictor, I got an almost straight line instead of the expected sigmoid curve.

What can be the reason for this?

  • 1
    $\begingroup$ The logistic ("sigmoid") curve is very close to straight in the region between (roughly) $-3/2$ and $3/2$. Within that region the probabilities will vary from less than $0.20$ to greater than $0.80$. Thus, when all predicted probabilities are within that range, necessarily the plot will look almost linear. Also, because this curve is differentiable, it is guaranteed to look almost straight over short enough sections, regardless of the typical predicted probabilities. Please, then, edit your question to provide more details about the shape and range of that plot. $\endgroup$ – whuber Apr 12 '14 at 19:33

One reason is that the predictor doesn't have a very big impact on the binary response. What was the p-value of the predictor when output by the regression? If it was high, that would explain it.

Alternatively, if you didn't specify the link function properly whatever software you're using could be using an identity link function (which is not, strictly speaking, logistic regression in that case).

Otherwise we'll need more information to diagnose.


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