I'm trying to run a regression on Likert (1-5) data. My dependent variable $Y$ is customer satisfaction and the 10 independent variables are ratings of various attributes (price, ease of use, etc.). The data come from a survey. The problem is, everyone is either satisfied (300/800) or very satisfied (450/800), making the data extremely left-skewed. The $X$'s also more or less behave like that.
The results of the regression seem sensible, but I keep wondering if it's justified to run in on data like that. I know that linear regression only requires that the residuals be normally distributed (which they are), but I thought skewness messes with OLS (I'm doing this in
R with the
lm function, perhaps it automatically takes care of that?)
I don't think it makes sense to apply any transformations to an ordinal scale like that, but I feel uneasy about my results and am wondering how they could be improved? I'd like to stick to a linear model if possible, because that's what I'm most familiar with. What should I look into? Any suggestions or references are welcome.
If a linear model is really not salvageable, I'm guessing I should try some kind of ordinal regression - would be grateful for any advice on the best way to go about that in
EDIT: I should add that I'm mostly interested in qualitative results, i.e. which attributes are significant and how they roughly rank.