According to Filzmoser et al. 2009, the best way to conduct a principal component analysis for compositional data with outliers is:

• using a robust PCA method
• and using the isometric log ratio transformation (instead of the centred log ratio transformation, see also the discussion here).

The function pcaCoDa() from the R package robCompositions can do both things.

However, every time I run the function, I get a different result... how is that possible?

Also, for what I understand checking help(pcaCoDa), the data set that you provide to the function must not be transformed - the transformation is done internally. But how about scaling? Should we scale the matrix before running the pcaCoDa() if the different columns use very different units?

According to Filzmoser et al. 2009, the best way to conduct a principal component analysis for compositional data with outliers is:

• using a robust PCA method
• and using the isometric log ratio transformation (instead of the centred log ratio transformation, see also the discussion here).

The function pcaCoDa() from the R package robCompositions can do both things.

However, every time I run the function, I get a different result... how is that possible?

Examples from four different runs:

In some of the biplots above, it's just a matter of the components being rotated, but for others, I don't think that's the case.

Also, for what I understand checking help(pcaCoDa), the data set that you provide to the function must not be transformed - the transformation is done internally. But how about scaling? Should we scale the matrix before running the pcaCoDa() if the different columns use very different units?