# Ordinal vs. Multinomial Logistic Regression?

Dear Esteemed Experts
For a study with the outcome is the disease severity classified in 3 levels as follows:

“Stationary”, “Active”, “Aggressive”

Should I use multinomial or ordinal logistic regression ?

If you see this StackExchange post it seems that ordinal regression is more appropriate, as there is ordering of the levels. See also @f2harrell’s comment to this reply which seems to confirm that ordinal would be appropriate.

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Once the sample size gets huge, since there are only 3 levels, you can use multinomial to avoid assumptions. Make sure that the underlying process is really discontinuous though, because you are modeling it as discontinuous.

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Thanks Dr @f2harrell, just one more question

since there are only 3 levels

Based on your experience, would you suggest multinomial also with 4 levels or 5. Is there a way to be able to judge when is appropriate to go for ordinal ?

The number of slopes required in a multinomial logistic regression model is (k-1)p where k is the number of distinct Y leves and p is the number of predictor degrees of freedom. When k=3 you are doubling the number of parameters when compared to an ordinal logistic model. When k>3 it gets a little out of control and requires very large samples.

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@f2harrell So If I am going to work with 4 ordinal outcomes, I shall start with Ordinal regression ? Then if the assumptions of proportional odds are not met I have to work with multinomial model?

The answer is very nuanced. There is a high cost of not assuming proportional odds, and when the sample size is below a certain level estimates from assuming PO will be more accurate than estimates from a multinomial model. See details at Assessing the Proportional Odds Assumption and Its Impact which also goes through the new R `rms` package function `impactPO` which assists in measuring the impac of the PO assumption.

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