Conditional quantiles are a very useful way of considering model
performance against observations for continuous measurements (Wilks, 2005).
The conditional quantile plot splits the data into evenly spaced bins. For
each predicted value bin e.g. from 0 to 10~ppb the corresponding
values of the observations are identified and the median, 25/75th and 10/90
percentile (quantile) calculated for that bin. The data are plotted to show
how these values vary across all bins. For a time series of observations
and predictions that agree precisely the median value of the predictions
will equal that for the observations for each bin.The conditional quantile plot differs from the quantile-quantile plot (Q-Q
plot) that is often used to compare observations and predictions. A
Q-Q~plot separately considers the distributions of observations and
predictions, whereas the conditional quantile uses the corresponding
observations for a particular interval in the predictions. Take as an
example two time series, the first a series of real observations and the
second a lagged time series of the same observations representing the
predictions. These two time series will have identical (or very nearly
identical) distributions (e.g. same median, minimum and maximum). A Q-Q
plot would show a straight line showing perfect agreement, whereas the
conditional quantile will not. This is because in any interval of the
predictions the corresponding observations now have different values.
Plotting the data in this way shows how well predictions agree with
observations and can help reveal many useful characteristics of how well
model predictions agree with observations --- across the full distribution
of values. A single plot can therefore convey a considerable amount of
information concerning model performance. The conditionalQuantile
function in openair allows conditional quantiles to be considered in a
flexible way e.g. by considering how they vary by season.
The function requires a data frame consisting of a column of
observations and a column of predictions. The observations are
split up into bins according to values of the
predictions. The median prediction line together with the 25/75th
and 10/90th quantile values are plotted together with a line
showing a perfect model. Also shown is a histogram of
predicted values (shaded grey) and a histogram of observed values
(shown as a blue line).
Far more insight can be gained into model performance through conditioning
using type. For example, type = "season" will plot
conditional quantiles by each season. type can also be a factor or
character field e.g. representing different models used.
See Wilks (2005) for more details and the examples below.