Contradicion in cross validation plots

Question

The cross validation plot shows that high measurements (~between 3 and 5) are overestimated (blue line below grey, predicted on x-axis, measured on y-axis):

The standardized error plot indicates underestimation for the same data and value range (~between 3 and 5):

I may misinterpret these plots, but this seems contradictory.

The cross validation was carried out in ArcGIS Pro 2.5.0.

Thanks!

Christian

cNeuwirth · Answer

The unstandardized error plot has also a negative slope:

Which in turn contradicts a slope < 1 in the unstandardized predicted-measured plot:

Some outliers may have been ignored in the regression (sigma > 2). But why only in this plot?

Christian

Eric6346 · Answer

Hi again,

You're correct that in ArcMap, the Measured value appears on the x-axis, but this was changed for ArcGIS Pro, based on new research in 2008.  You can read the full details of why the Measured value should be on the y-axis in this paper.  Long story short, the axes don't matter for the R^2 value and for testing whether the slope is equal to 0.  However, to test that the line has slope=1 and y-intercept=0, the predicted values need to be on the x-axis and measured values on the y-axis.  This is only relevant for Measured vs Predicted, so we kept the Measured value on the x-axis for all other graphs.

I'm still interested to hear whether the Error plot also has a negative slope.  These are the raw errors that are not standardized by the kriging variance, so that graph may still have a positive slope even if the standardized errors have a negative slope.

-Eric

cNeuwirth · Answer

Hi Eric,
thanks for your detailed explanations! I agree that the blue line is the problem. It seems like the regression does not properly represent the point cloud. Your explanation (outliers > 2 standard deviations ignored) makes sense though. However, this makes results quite counterintuitive. Particular because the same procedure appears to have not the same effect in the standard error plot causing some ambiguity.
Moreover, in older version of ArcGIS the cross validation plot showed ‘predicted’ on the y-axis and ‘measured’ on the x-axis. This is why I expected some kind of bug.
Regards,
Christian