Hi Mike,
In PCA of residuals what does it mean when some items have zero or near zero loadings on the first contrast?
Does it mean that they measure neither the target dimension nor the secondary dimension?

thanks

Raschmad, when the data fit the Rasch model, then the response residuals will look like normally distributed noise. We expect the items to have loadings near zero on the first  and subsequent contrasts.

Zero loading on a contrast means "the residuals for this item are not correlated with the hypothetical component underlying the contrast."