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I have a regression problem where one of the explanatory variables is categorical with 2 categories. My issue is that one category has 90% of the observations and 2nd category has only 10% observations.

Does the presence of such a highly unbalanced categorical variable pose any problem on the statistical inference of the model coefficients?

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  • $\begingroup$ @StephanKolassa Judged too fast, on closer inspection I agree it is not a good duplicate. $\endgroup$
    – Frans Rodenburg
    Commented Aug 7 at 13:42

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The standard error of the parameter estimate for your categorical predictor will be larger than if the factor levels were balanced. Therefore, you will need to observe a larger effect size to be able to declare statistical significance. All this will be handled automatically in your software.

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    $\begingroup$ Thanks for your answer. However I am not clear on the part how exactly software will handle this? How software will know exactly that data is unbalanced? Does it use any threshold type? My original problem is logistic regression with some predictors and one of them is such unbalanced categorical variable. How R would manage this automatically? $\endgroup$
    – Bogaso
    Commented Aug 7 at 13:30
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    $\begingroup$ The software will calculate standard errors, and these will be larger than for a balanced predictor. The t/z statistics will be calculated automatically based on the parameter estimates and the standard errors (so t/z will be smaller than in the balanced case, keeping the parameter estimate constant), and p values will be derived from the t/z values. The output in summary() or similar will automatically account for your predictor imbalance. There is really nothing you need to do. (Except keep in mind that your parameter estimates are less precise.) $\endgroup$
    – Stephan Kolassa
    Commented Aug 7 at 13:36

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