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


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!


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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