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The result of discriminant analysis for the three classes are two discriminant functions LD1 and LD2.

In the case of two classes, there is one discriminant function LD1, and the threshold of discrimination can be calculated as follows: $$ C = \frac{1}{2}(M_{1} + M_{2}) $$ M1 is the mean value of LD1 estimates for class 1, and M2 for class 2.

Please, help me understand how, with LD1 and LD2, calculated threshold of discrimination for the case of three classes.

UPD

How I can find the equations of these thresholds lines on a graph?

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No. The threshold can not be "calculated" by that formula. That formula is one (!) possibility for setting that threshold.

There is an enormous amount of misinformation regarding thresholds for classification. I recommend reading this earlier thread. It does not explicitly address your three-level classification case, but can be applied to it: the solution is to think about your costs of misclassification and set thresholds accordingly.

Even better is to discard thresholds in the statistical analysis entirely and work with purely probabilistic predictions.

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  • $\begingroup$ Very grateful for your answer. It helped me a little to understand how I can use probabilistic prediction in my case. $\endgroup$
    – Vitalii
    Commented Apr 8, 2020 at 6:49

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