Hi List,

   Firstly, thanks Randy, for the clarification on behavioral PLS permutation testing,  I have one last question, which is more theoretical than mechanical. Specifically, when does it make sense to normalize one's PLS data? Here's why I ask ...

    I am doing a behavioral PLS on cortical thickness data, and of course, a huge amount of the variance at any one data point (vertex) is accounted for by individual differences in overall cortical thickness (some people have thicker cortex than others).  This is particularly salient since we are using native thickness values.  A PCA on the thickness values clearly pulls out overall thickness as the first component.

   When I do a PLS analysis using the un-normalized values, I get only 1 significant LV, accounting for 84% of the prop. of SSCB correlations.  When I do the same analysis using normalized values (I normalized by rescaling the values to a common mean, say, 100 units), I see 2 significant LVs, accounting for approx. 46% and 18% of the SSCB. Looking at and comparing the correlation plots, the patterns for LV1 and LV2 look very similar regardless of normalization, with some difference in error bar magnitude.  All LV2 correlations are in the same direction.

How does normalization affect the PLS analysis?  I would think that I would remove the variance attributable to overall cortical thickness.  Why do I get the same PLS LVs regardless of normalization. Why are two significant when normalized, and only one when not normalized?

Any suggestions would be very appreciated,

Thanks,

-Jim