In a linear regression, I have a number of predictors variables that are expressed as proportions. The outcome variable is continuous. My residuals are not normally distributed, with a mild to moderate positive skew.
Should I use a logit transformation on the predictor variables to see how this impacts the residuals?
If yes, I am having trouble understanding with what to do with my cases that have a proportion of 0.0 on some of the predictor variable (e.g. a case with 0% on a variable). In particular, I've been considering the advice of Papke and Wooldridge (1996) and Baum (2008) on how to deal with those sorts of cases when they are measured responses as opposed to due to structural issues. They suggest various options including winsorisation and something called fractional logit responses. However, they only discuss their options in terms of proportional outcome variables, and never in terms of proportional predictor variables. Are such approaches appropriate to proportional predictor variables in a linear regression?