I'm evaluating the error in three cross-validated models plotting observations against predictions. To do so, I'm comparing the RMSE (root-mean-squared-error) and the Pearson's R between predictions and observations.
(Note: negative binomial models, sample
n = 49,
mean = 13.33 and
SD = 17.27)
The results for the RMSE are 18.81, 18.97, and 17.48, respectively. Pearson's R are 0.10, 0.09, and 0.33.
How can I interpret this huge difference (~70%) in correlation values but with only minor changes (~10%) in RMSE? Am I right if I say that the third model performs much better in predicting extreme values than the other two? Essentially, I understand that in a prediction based on the mean the correlation would be 0 but the RMSE may not be so high due to over-predictions compensating under-predictions (?). Is there any other alternative?