Discriminability and uncertainty in principal component analysis (PCA) of temporal check-all-that-apply (TCATA) data

Sammendrag

Temporal check-all-that-apply (TCATA) data can be summarized and explored using principal component
analysis (PCA). Here we analyze TCATA data on Syrah wines obtained from a trained sensory panel. We evaluate
new and existing methods to explore the uncertainty in the PCA scores. To do so, we use the bootstrap procedure
to obtain many virtual panels from the real panel’s data. Virtual-panel PCA scores are obtained using two
methods. The first method, called the partial bootstrap (PB), obtains virtual-panel scores from regression. The
second method, called the truncated total bootstrap (TTB), applies PCA to the virtual-panel results to obtain
scores, which are truncated and superimposed on the real-panel scores by Procrustes rotation. We use the virtual
scores from each method to investigate uncertainty in the real-panel PCA scores visually and numerically. To
understand the uncertainty of the scores, we obtain confidence ellipses (CEs) and their areas, as well as confidence intervals (CIs) and their widths. Next, to determine whether PCA scores for different samples are well
separated, we propose a procedure for approximating the standard errors of sample differences and correcting for
multiple comparisons. We propose a discriminability index, and show that it can enhance the interpretability of
PCA results. We incorporate graphical features into our PCA biplots to visualize discriminability. We did not find
a large difference between the PB and TTB methods for understanding the uncertainty and discriminability in
PCA scores. Although the TCATA data that we analyzed have a special structure, the methodological approaches
presented here can be readily adapted to other applications of PCA.

Les publikasjonen her:

DOI : doi.org/10.1016/j.foodqual.202...
NVA : hdl.handle.net/11250/3034418