Direct Model Report
This section contains the reports that are available when you fit a direct model in the Functional Data Explorer platform.
Function Summaries
Shows summaries from the Functional PCA for each level of the ID variable. The functional principal components associated with eigenvalues that explain more than 1% variation in the data are displayed by default. The mean, standard deviation, median, minimum, and maximum are also shown.
Functional PCA
Functional principal components analysis (functional PCA) is performed on the fitted functional model. The Functional PCA report lists the eigenvalues that correspond to each functional principal component (FPC) in order from largest to smallest. The percent of variation accounted for by each FPC and the cumulative percent is listed and shown in a bar chart. There is a graph of the mean function as well as a graph for each shape function. These are the values of the eigenfunctions.
You can perform model selection in the Functional PCA report to refine the selected number of functional principal components. There is a solution path plot that shows the Bayesian Information Criterion (BIC) plotted versus the number of FPCs. The current number of FPCs is designated by the dotted vertical line in the solution path plot. It is possible that models with different numbers of FPCs might have similar fits. Therefore, the solution path plot provides zones, which are intervals of values of the BIC statistic. There is a green zone and a yellow zone. The green zone contains values in the interval of the minimum BIC to the minimum BIC plus four. The yellow zone contains values in the interval of the minimum BIC plus four to the minimum BIC plus 10. By default, the model with the smallest number of FPCs within the green zone is selected. You can drag the slider at the top of the vertical line to change the number of FPCs. Dragging the slider automatically updates the other information in the Functional PCA report.
Note: Narrow zones relative to the full y-axis scale can be difficult to view on your plot. Zoom in on the y-axis to better visualize the zones.
There is also an overall prediction plot and a grid of individual prediction plots. The grid of individual prediction plots has the same layout and controls as the grid of individual plots in the Data Processing report. At most, there are twenty plots shown at a time and there are drop-down menus and arrows that enable you to view different groups of individual prediction plots. Updating the number of FPCs automatically updates the prediction plots as well.
The prediction plots show the raw data and prediction curves that correspond to the current model. If there is a validation set, the predicted curves are not shown for functions that are in the validation set. The curve in the overall prediction plot is a prediction of the mean curve, given the specified number of FPCs. The curves in the individual prediction plots are prediction curves for each specific function, given the specified number of FPCs.