I am performing a regression where my dependent variable is the value of a group's Simpson Diversity Index. This index value is constrained by $1/k$ and $1$ (where $k$ is the number of classes), though none of my values approach $1$. I know OLS regression is not suited for regression with a 'bounded' dependent variable, and my research on the appropriate method has pointed me in several directions, to include a logit transformation and a beta regression. Beta regression is well over my head, so I am considering the logit transformation, but still am looking for some advice on interpreting the resulting coefficients, and if this method is truly sufficient.
Additionally, some other questions: Do I just transform the dependent variable and leave the independent variables alone? Do I transform both? (By the way, my dependent variables include percentages, integers, and dummy variables.)
With the transformation, I have read that OLS would then be appropriate, but I have also seen suggestions for GLM.