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I have a simple confusion regarding the interpretation of logistic regression. Suppose married people are more likely to be employed compared to single people. In here, unemployment = 0, employment = 1. Similarly, married = 1 ,and single =0. Assuming odd ratio = 2. Can we say "Married people have 2 times higher odd of being employed compared to single PWDs." ? (here , I have use "odd" only instead of "odds" generally, which I have seen in many literature) So, do I have to use "odds" instead of "odd", it is okay if I used "odd" only?

utobi
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Prasanna
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In statistics the "odds" (not "odd") of something has a very particular meaning: is the probability of it happening divided by the probability of it NOT happening. So if something has a 70% chance of happening then the odds of it happening are 2.3 (70/30). This isn't how everyone else always uses the word "odds" but that's what it means in statistics. An odds ratio is what you get when you divide one odds by another - it's how much the odds (NOT the probability) of the thing have changed. So in your case, you can correctly say "Married people have 2 times higher odds (or "twice the odds") of being employed compared to single PWDs."

However, this does NOT mean that Married people are twice AS LIKELY to be employed. This is very common mistake about odds ratios - they don't tell you how the probability of something changes (the "risk ratio"), only how the "odds" have changed. And these are two different things - sometimes VERY different. If you want to know how the probability of being employed changes, then you need to provide some additional information about the baseline probability of employment. This can be done by computing average marginal effects or predicted probabilities from the underlying model.

Graham Wright
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    'This isn't how everyone else always uses the word "odds"'; other than completely qualitative uses ("the odds are good (bad)"; "may the odds be ever in your favour"), who uses "odds" in a different sense? This is exactly the sense it's used in gambling ... – Ben Bolker Jul 31 '23 at 16:30
  • People use "odds" to just mean "probability" all the time. Here's an example : https://floridapolitics.com/archives/625531-ron-desantis-odds-of-winning-2024-presidential-election-slip-to-5/ – Graham Wright Jul 31 '23 at 16:48
  • fair enough .... (especially since you said "always uses" ...) – Ben Bolker Jul 31 '23 at 17:00