Difference in PCA Loadings Between Two Fits

Compares the variable loadings of two independently-fit prcomp objects on the same set of variables (e.g. the same domain's data fit at baseline vs. at a later timepoint), matching components positionally (both fits' PC1, both fits' PC2, ...).

Usage

pca_loading_diff(pca_baseline, pca_comparison, n_components = NULL)

Arguments

pca_baseline

A prcomp object treated as the reference.

pca_comparison

A prcomp object to compare against pca_baseline, fit on the same (or overlapping) variables.

n_components

Number of leading components to compare. Defaults to NULL, meaning all components shared by both fits.

Value

A tibble with one row per shared variable (feature column) and one column per compared component (PC1, PC2, ...) holding the sign-aligned difference (comparison minus baseline).

Details

PCA loading vectors are only unique up to sign: a component can flip orientation between two otherwise-equivalent fits without changing the pattern it represents. Naively differencing loadings would then show a spuriously large change (up to roughly double the loading) for a component that hasn't meaningfully changed at all. To avoid this, for each shared component pca_comparison's loading vector is sign- aligned to pca_baseline's: it is flipped (multiplied by -1) if doing so reduces the total absolute difference across variables relative to leaving it as-is. The difference is then computed as (sign-aligned comparison) minus baseline.

Variables are matched by name (the rownames of $rotation). If the two fits were built on different variable sets, only the intersection is used; no error is raised.

Examples

set.seed(1)
baseline <- prcomp(mtcars, center = TRUE, scale. = TRUE)
comparison <- prcomp(mtcars[sample(nrow(mtcars)), ], center = TRUE, scale. = TRUE)
pca_loading_diff(baseline, comparison)
#> # A tibble: 11 × 12
#>    feature       PC1       PC2       PC3       PC4       PC5       PC6       PC7
#>    <chr>       <dbl>     <dbl>     <dbl>     <dbl>     <dbl>     <dbl>     <dbl>
#>  1 mpg      5.55e-17 -5.55e-17 -8.33e-17  4.41e-16 -2.55e-15  1.21e-15  5.50e-15
#>  2 cyl      1.11e-16 -2.78e-17 -4.72e-16 -3.20e-16  3.40e-16  3.05e-16  1.37e-15
#>  3 disp     1.11e-16  4.86e-17  2.91e-16  3.89e-16 -2.33e-15  3.55e-15  1.94e-16
#>  4 hp       1.11e-16  3.61e-16  6.38e-16  1.10e-15 -6.66e-16  4.04e-15  1.91e-16
#>  5 drat     0         0         0        -3.33e-16  3.19e-15  1.53e-15 -8.47e-16
#>  6 wt       1.67e-16 -5.55e-17 -1.67e-16  1.94e-16 -2.64e-15 -3.89e-16  1.38e-15
#>  7 qsec    -2.78e-17 -1.11e-16  2.22e-16  2.08e-16 -3.19e-15 -1.39e-15  2.55e-15
#>  8 vs      -1.11e-16 -2.78e-17  5.55e-17  4.72e-16  2.11e-15  3.69e-15 -1.28e-15
#>  9 am      -5.55e-17  1.11e-16  2.50e-16  7.08e-16 -3.50e-15 -1.44e-15  1.44e-15
#> 10 gear    -2.78e-17  1.67e-16  0         5.55e-17 -2.91e-15  1.64e-15 -1.67e-15
#> 11 carb     5.55e-17  0        -1.11e-16 -6.11e-16  1.67e-15 -3.19e-15  2.80e-15
#> # ℹ 4 more variables: PC8 <dbl>, PC9 <dbl>, PC10 <dbl>, PC11 <dbl>