Devise measure of trait prediction quality: NMSE

[richelbilderbeek]

The MSE between the predictions and identity line works nice.

That is, when the actual values have the same variance:

[richelbilderbeek]

From me:

I guess after normalization, I guess it is neutral to use the root or the non-root value itself...?

From Torgny:

Well, that's because it can be discussed in relation to a standard error or standard deviation, I suppose. The mean-square-error (MSE) is more of a variance. In fact, the MSE is a measure of the variance + the squared bias of your predicted values. So, if your prediction is unbiased, your MSE is just the variance!

I should say that MSE in your case may be thought of as a measure of the "average" variance + the "average" bias. I suppose that your variance and/or your bias could, hypothetically speaking, change across the range of your true values...?

If you plot the data (true vs. predicted), you would see whether this would be the case, e.g., if the predicted data are more scattered for higher values of your true data (increased variance), or, e.g., if the predicted data begin to deviate from the identity-line (increased bias).

[richelbilderbeek]

Done!