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I'm aware that Logistic Regression works in odds, not probabilities. More specifically, it reports the variables in how they increase or decrease the odds. That makes sense, but when I think about it more, I'm wondering do probabilities really work like this in real life examples?

So if there is a variable with a large coefficient (say smoking for cancer), does it really only increase the probability of a cancer from 1 to 1.5% for people with low probability but 50 to 60% for mid-probability (see table below)? It just doesn't sit right.

I'm finding logistic regression tricky to present to business stakeholders because of this. When asked how certain variables change the probability, the answer that it depends on the underlying probability doesn't seem very satisfying.

If anyone could help clarify things that would be great!

odds        p       odds (50% increase) new p
0.01010101  0.01    0.015151515         0.014925373
0.176470588 0.15    0.264705882         0.209302326
0.428571429 0.3     0.642857143         0.391304348
1           0.5     1.5                 0.6
2.333333333 0.7     3.5                 0.777777778
5.666666667 0.85    8.5                 0.894736842
99          0.99    148.5               0.993311037
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    $\begingroup$ You're correct. So: explain the results in terms of odds! $\endgroup$
    – whuber
    Mar 12, 2018 at 22:07

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Edited to better address question

You can use the inverse logit to convert from odds to probability; inverse logit predictions not coefficients. Missed the point of your original question, sorry. I have added the link to a related question in comments.

More related to your actual question of how to convey the information. Plot predictions against your covariates and show them visually. Visually showing the trend of probability against a chosen covariate may allow stakeholders to understand the relationship. My understanding is that stakeholders are not interested in the math or the statistics, just the trend. So why bother explaining the math.

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  • $\begingroup$ See google.com/url?sa=t&source=web&rct=j&url=https://… $\endgroup$ Mar 13, 2018 at 2:53
  • $\begingroup$ Re "inverse logit": Isn't the point of the question that interpreting the model in terms of probability is complicated? $\endgroup$
    – whuber
    Mar 13, 2018 at 15:04
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    $\begingroup$ Yes, noticed that after initial response. Thus, I have added the link to a related question and stated that visually showing the trend of probability against a choosen covariate may allow stakeholders to understand the relationship. My understanding is that stakeholders are not interested in the math or the statistics, just the trend. $\endgroup$ Mar 13, 2018 at 15:09

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