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I hope this is not too basic a question but, for logistic regression, does the one in 10 rule of thumb (I'm aware there is some debate around 1: 10, 15, 20, other measures) apply within categories?

i.e. I am looking at obesity and an outcome in a dataset of 16,000, people are divided into normal weight (n = ~7k), overweight (~6k), obese 1 (~2k), obese 2 (600) and obese 3 (n=188) groups (1 x categorical variable). I also have some other independent variables which are less relevant here. Anyway, with obese 2 and 3, both n and incidence reduce from 125 cases in 6k to 15 cases in 600 (obese 2) and 4 cases in 188 (obese 3). Subsequently, the CIs are very large for obese 2 and obese 3, so I am wondering if this is because of a lack of power and whether the rule of 10 also applies within a category (i.e. within obese 2/3) within the overall regression?

Thank you in advance for your help and ideas!

Marie NiDhu
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    I am not familiar with the “one in 10” rule or its purpose. I’m familiar with some other stuff though. Can you tell me more about the rule in your question? Perhaps I understand the idea under a different label. – EngrStudent Nov 29 '21 at 12:17
  • https://stats.stackexchange.com/questions/163055/clarification-on-the-rule-of-10-for-logistic-regression thanks for your comment! my understanding is that you need n=10 in the case group for every independent variable. For my normal weight groups i have enough cases but in obese 2/3 there are a lot less cases and I wonder is this why they are non-sig (despite similar OR to obese 1 group which was significant)... I'm a bit stuck so would appreciate any thought you might have! – Marie NiDhu Nov 29 '21 at 12:29
  • https://en.wikipedia.org/wiki/One_in_ten_rule might be relevant – Henry Nov 29 '21 at 12:37

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The multiple categories, when one hot encoding is used, is multiple applications of nominal regression. If the rule is that the minimum samples of the smaller class is 10 (15, 20, …) then of course it can applies In the multi class case.

As with all heuristics, a.k.a. rules of thumb, it is a guideline and not a mandate. The good judgment of a practitioner can sometimes direct them to transgress this rule, And still lead to valuable results.

If there were three classes instead of two, then the classifier is really three classifiers, and the minimum members of the smallest class between each pair would still be preferred to be 10. If our classes are “A“, “B“, and “C“, Than we have three regression: “A” versus the rest, “B” versus the rest, and “C” versus the rest. In each of those regressions the heuristic wants the minimum sample size to be larger than 10 (15, 20, …).

(Personal story) In the real world I have run into cases where I have to work with a minimum sample size of one. It wasn’t fun. It wasn’t fair. But it is what I had. The only way to attack that particular problem was domain knowledge: I deconstructed the physics of the problem and then use those to construct synthetic samples. It worked, and after it ran for a while I was able to get many more samples and improve things, but it is not (!) an ideal road. It is actually the second toughest case.

EngrStudent
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