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I have trained a model that predicts a multinomial output (a.k.a. multi-class classification). Would anyone know how the accuracy can be measured?

The target takes one of the following values: "Yellow", "Red, "Green", or "Blue".

I know that for binomial targets, ROC/AUC provide a good solution. But I haven't found anything for my problem.

gung - Reinstate Monica
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Faz
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    Presumably if the target is 'green' then 'red' and 'blue' and 'yellow' are considered equally inaccurate (you don't specify). If that's the case, then you're effectively just in a binomial situation - in each case, either it got in the right category or it didn't. – Glen_b Jan 23 '14 at 00:49
  • Thanks a lot for the reply. Yes, in my case any mis-classification is equally inaccurate. However, in case of binomial output, we use the raw pronsities (probability of positive outcome) to consutruct the ROC curve and hence calculate the AUC. In a multinomial case as this one, I do not have raw propensities. So the best thing that I can think of is using the rate of misclassifications to assess a models accuracy. But if anyone knows a stronger method (like AUCs for binomial), please do let me know. – Faz Jan 24 '14 at 16:45
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    Can you define 'raw propensity' for me (google was no help)? You may find searching for things like 'multiclass ROC' or 'multiclass AUC' here (and more widely) gets some hits, such as [this answer](http://stats.stackexchange.com/a/2155/805) – Glen_b Jan 24 '14 at 23:25

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