  PCA is often used to visualize data when the rows and the columns are both of
interest. In such a setting there is a lack of inferential methods on the PCA
output. We study the asymptotic variance of a fixed-effects model for PCA, and
propose several approaches to assessing the variability of PCA estimates: a
method based on a parametric bootstrap, a new cell-wise jackknife, as well as a
computationally cheaper approximation to the jackknife. We visualize the
confidence regions by Procrustes rotation. Using a simulation study, we compare
the proposed methods and highlight the strengths and drawbacks of each method
as we vary the number of rows, the number of columns, and the strength of the
relationships between variables.
