My data have three levels. The highest level is preferred vs. actual state. For each state there are 6 dimensions. Within each dimension there are 4 variables representing scores of 4 kinds of leadership style. At this lowest level each style is given a score so that the sum of scores add up to 100 for all 4 styles within the respective dimension.
I need to address two issues:
1) What is the most appropriate and parsimonious analysis of such data?
2) As the scores add up to 100, they are presumably negatively correlated for each participant. What difference this may or may not make?
You are correct that the variables will be negatively correlated because they are not independent of each other. Unfortunately, almost all forms of multivariate analysis require that the measures be independent.
I hope someone else can suggest a way for you analyze this data, because most of the traditional approaches will not work.
Perhaps ask a specialist for compositional data, such as
https://www.researchgate.net/profile/Vera_Pawlowsky-Glahn
how to approach multivariate analysis of such data or look yourself for relevant papers:
http://scholar.google.de/scholar?q=%22compositional+data%22+multivariate .
There exist some transformations, so called log-ratio transformations. Comparing them all have their pro's and cons's. Try out package compositions or robCompositions that include a lot of methods for such kind of data.
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