My quesion is  to find out which fixed factors (and cross-level interactions) had the strongest effects. I know as per Snijders and Bosker there are methods by which to extract effect sizes for these nested structures (e.g., using the variance components for  PRE statistic), but many examples I've seen are for single- predictor models.
Where I am stuck is how to rank-order magnitude of effect for individual variables when you have multiple predictors and/or cross-level interactions (i.e., time varying x time invariant interaction).  I'm assuming that similar to the problems encountered when rank ordering strength of explanatory variables in linear or logistic regression models,  one needs to factor in the extent of collinearity (which dominance analysis and relative weights does).

Somebody suggested standardizing all of the explanatory variables and then rank ordering (or squaring) the fixed standardized coefficients, but this does not address the extent of collinearity.  I was thinking of possibly freeing up the stochastic parameters for each of the fixed predictors and using those as a PRE statistics, but when I have done so for multiple predictors the model tends to implode (took over 1000 iterations in HLM7.0!).

So I was curious how to address the relative importance of multiple predictors/effect sizes (and partitioning of variance) for a random coefficient model,  and whether it be of a cross-sectional or longitudinal design?

Thank you very much.