Dear Cross Validated Users,
I am addressing myself to you with a question for which I couldn't find an answer despite intensive googling. I want to run a regression with a multitude of independent variables. The independent variables can be grouped into groups of highly correlated variables. I want to be able to interpret the results, thus I would like to apply some kind of dimension reduction method to the individual variable groups. Intuitively I would apply a PCA to each group and use the resulting principal component for each group as an explanatory variable in the final regression. I would thus get the 'optimal' weighting of variables within each group and be able to interpret the coefficients of the artificially (by dimension reduction) created summarizing variables. Is there some method which does what I want?
I am grateful for every comment!
Background: I am measuring different network statistics of a dynamic network with different window sizes from which I want to estimate different dependent variables. Unfortunately there is no way to tell which window size is the correct one. So I am computing the network statistics over a number of different window sizes. I want to create some kind of surrogate explanatory variables for each network statistic over all available window sizes.