How to evaluate models: Observed vs. Predicted or Predicted vs. Observed?

PIÑEIRO, G.,; PERELMAN, S.; GUERSCHMAN, J.P.; PARUELO, J.M.

ECOLOGICAL MODELLING

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2008 vol. 216 p. 316 - 322

0304-3800

A common and simple approach to evaluate models is to regress predicted vs. observedvalues (or vice versa) and compare slope and intercept parameters against the 1:1 line.However, based on a review of the literature it seems to be no consensus on which variable(predicted or observed) should be placed in each axis. Although some researchers think thatit is identical, probably because r2 is the same for both regressions, the intercept and theslope of each regression differ and, in turn, may change the result of the model evaluation.We present mathematical evidence showing that the regression of predicted (in the y-axis)vs. observed data (in the x-axis) (PO) to evaluate models is incorrect and should lead to anerroneous estimate of the slope and intercept. In other words, a spurious effect is added tothe regression parameters when regressing PO values and comparing them against the 1:1line. Observed (in the y-axis) vs. predicted (in the x-axis) (OP) regressions should be usedinstead. We also show in an example from the literature that both approaches producesignificantly different results that may change the conclusions of the model evaluation.