I'm running regressions on a 2,336 respondent data set from an organizational survey with mostly ordinal response scales (1-5, yes/ no, etc.). I factor analyzed ~130 survey items and boiled that down to ~10 dependent variables I'm interested in examining and 23 independent variables (each made up of 2-6 survey items). I standardized the item scores, then averaged the standardized item scores that make up a variable for entry into the regression. I then ran LM regressions in R on each independent variable separately with the 23 independent variables in each regression.
That’s the context, now for my question. The regression results show the beta weights, their significance, and their Relative Importance. What surprises and confuses me is that an independent variable with by far the highest Relative Importance (34%) has a very low beta (0.01) and no statistical significance in the regression. On the other hand, some large beta coefficients with great significance (<<0.01) but have very low Relative Importance (e.g., 2%). I should think high beta/ high significance coefficients would tend to be the variables with the greatest Relative Importance. Sometimes they are in some regressions, but not in others.
I need to understand how these calculations are done to understand why there’s this unexpected difference. That is the point of this assignment: to help me understand what's going on under the covers that's giving me these results--and then to help me make sense of these results.
I'd also like to confirm the methods I am using will provide the best assessment of how these independent variables are related to the dependent variables. At this point, I am not looking for someone to carry out the statistical analysis itself. I am looking for someone to spend possibly 1-2 hours examining what I've done and explaining to me why/ how I am getting the results I am getting. And to advise on any different approach that might be suited to my needs. I will share data and analysis results.
The person I'm looking for must have an in-depth understanding of the mathematics involved, not just how to use a stats package (as I said, I'm using R). I have a background in statistics and taught stats at the introductory undergraduate level, but that was 40 years ago and so I don't have either a sharp memory of what once I understood, nor an understanding of developments in statistical analysis since then relevant to my situation. But, I can follow clear explanations, which is what I'd like to pay someone to provide.