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I am trying to understand why standard errors are negatively affected by choosing a reference category with a small N.

Example

Model: Logistic regression

Outcome: Smoking (Yes vs No)

Independent variable: Race (NH White, NH AA, NH Other, Hispanic)

Normally, I would choose the reference category with the largest N (in this case NH White), but I am trying to justify why that is an appropriate decision.

Any insight is appreciated!

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The odds ratio compares two odds (by computing the ratio of the odds). If one of those odds is measured with a lot of uncertainty (e.g. because of small N), then the ratio of the two odds will also be measured with a lot of uncertainty. So if your reference category is small N, then all the odds ratios will have large standard errors.

It does not change your fundamental model: you can from the parameter vector and the variance covariance matrix compute the odds ratios and standard errors for other contrast and you will get the same (smaller) standard errors.

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