We have fitted a multilevel multinomial logistic regression model to our data. We have obtained relative risk ratios(RRR). For most of the independent variables RRR have usual values, like 0.49, 0.78, 2.45, 1.78, etc. But, only for a ordinal variable which has three categories, one of the categories have RRR value 115590.5. Why is it that much large and unusual values than the rest of the RRR values obtained by fitting the multinomial logistic regression model? Have you ever found such a big number as RRR? What could be the possible reason behind it?
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2$\begingroup$ Is that category very rare, and are many more cases in that category in the target class than in other categories? $\endgroup$– Stephan KolassaCommented Jan 31 at 14:07
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A risk ratio looks like
$$ RR=\dfrac{Pr(Y\mid X=a)}{Pr(Y\mid X=b)} \>.$$
What happens when $Pr(Y\mid X=b) \rightarrow 0$? The answer is that the risk ratio approaches infinity.
What is very likely happening, assuming there is no coding error, is that your reference risk (whatever is in the denominator of your risk ratio calculation) is very very small, hence the large risk ratio.
answered Jan 31 at 14:33
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$\begingroup$ Agree this is likely the case, although it's a little unexpected that only one of the three categories has a very high RRR. You'd typically expect two of the categories to have high RRR when compared to the same tiny denominator, so this may additionally imply that two of the categories have tiny absolute risk. $\endgroup$ Commented Jan 31 at 14:46