# Why do we plot observed probability vs predicted probability when calibrating a logistic prediction model?

I'm trying to wrap my head around why predicted probability is plotted on the x-axis and observed probability on the y-axis, and not the other way around.

• Convention only: the (or rather one) convention is, I take it, that the observed response or outcome belongs on the $y$ axis; therefore anything else belongs on the $x$ axis. I've seen fitted on $y$ versus observed on $x$ too. Sep 6, 2016 at 18:14
• Possible duplicate: stats.stackexchange.com/questions/123938/… Sep 7, 2016 at 5:04
• I don't think they are duplicates. The linked question deals with scatter plots in general, while this question deals with a predicted versus observed quantity. Sep 7, 2016 at 12:56
• A perhaps related point is that residuals are conventionally defined as observed $-$ predicted or fitted, so points with positive residuals plot above the observed $=$ predicted line. I'd call that a very strong convention, while noting that Gauss defined residuals the other way round and that the convention is immaterial for sum of squared residuals or sum of their absolute values and so forth. Jan 26, 2018 at 9:30
• There seems to be a use for calculating fitting statistics that should be done regressing the OP (predicted on x-axis) explained in a paper They argue that for example you should not use the root mean square error (RMSE) for PO to show model performance. For visual explanation for me it is matter of personal preference but to get fitting statistics it has to be evaluated on OP (or you have to adapt the measures) Although r^2 will remain the same. Jan 26, 2018 at 10:24

We're used to thinking of the response variable on the $Y$ axis. The observed probabilities are responses in that sense.

The explanatory / predictor variables go (by convention, if you like) on the $X$ axis. The predicted probabilities are a [non-stochastic] function of the explanatory / predictor variables.

The mapping between a standard plot, like a scatterplot, and the plot you describe is straightforward to me.