Model Details

A range of graphical results for the prediction models are available depending on what View option was used.

Principal Component and CCA Modes

• Scree Plots.

  These plots show the percentage of variance explained by each X and Y mode. The percentages are shown for all modes regardless of the numbers that were specified for use. The plots can be useful in selecting the appropriate number(s) of X or Y modes to retain. One method for selecting the number of modes involves identifying "elbows" in the scree plot. The number of modes up to, but not including, the elbow are retained on the basis that the additional modes explain similar amounts of variance, which are assumed to be largely noise. Elbows are often easier to identify when the percentage variance is plotted on a logarithmic axis. An option to use logarithmic axes is available by right-clicking on the scree plots and using the Customise option. Another method for selecting the number of models is to compare the explained variance of each mode to that expected from random data. A computationally and conceptually simple such approach is based on the random stick theorem, which involves randomly dividing the total variance into segments and considering the expected size of the n th largest segment. The sizes of the random stick segments can be included on the scree plot by an option available by right-clicking on the plot. The broken stick will only show if the axis is linear, and the graph is not cumulative.

• Loadings and Scores.

  If gridded/station data are used, a map of the spatial loadings for each mode is shown together with the temporal scores. If forecasts have been made, the score(s) for the X modes are shown as bold crosses on the temporal scores graph. The loadings are shown in the form of correlations between the original gridded/station data and the temporal scores. If the data are unreferenced, a bar chart of the correlations is shown instead. If the loadings are saved to an output file, the actual loadings are saved rather than the correlations shown in the map. The graphics for each mode can be cycled by using the arrows at the top left of the graphics window, or by typing in the requisite number. Depending on your computer speed, you may need to wait a short time for the new graphics to display.

• CCA Maps.

  The CCA maps (or bar charts if the data are unreferenced) show similar results to the Loadings and Scores, but show the correlations between the original gridded/station/index data and the temporal scores for the corresponding X and Y components of the CCA modes together. The corresponding X and Y temporal scores are shown on the centre graph (the red line is for the X variables, and the green line is for the Y variables). It is the correlation between the curves on this central graph that CCA attempts to maximise. If forecasts have been made, the score(s) for the X component of the CCA modes are shown as bold crosses on the temporal scores graph. Again the loadings and scores for different CCA modes can be displayed using the control at the top left of the CCA maps window. As with the X and Y loadings and scores, the results can be saved to an output file, but the actual weights are saved rather than the correlations between the original gridded/station/index data and the temporal scores for the corresponding X and Y components of the CCA modes. The weights are known as "homogeneous maps" (even for unreferenced data).

Regression Models

If Multiple Linear Regression (MLR) , Principal Components Regression (PCR) or General Circulation Model (GCM) is used, the regression equation(s) for estimating the value of the Y variable using the X variable(s) are shown. If there is only one X variable, a graph will also be shown comparing the predictor with the predictand. This graph is different to that shown in the Scatter Plot : the scatter plot compares the cross-validated predictions with the observations, whereas the Regression Plot compares the predictors with the observations.

The titles of all graphs can be customised by right-clicking on the graph. The data can be saved using the File~Output Results menu item.