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.
Best Answer
Do you have any values of the response that are exactly 0 or 1? (those will cause problems with a logit transform)
Have you tried plotting your data? What exploratory techniques have you used? What have other researchers in the area done?
You could try simulating some data that fits with a logit transform or a beta regression model (or anything else that you consider trying) and see how that compares to your data to get a better feel for which model may be more appropriate.
With what you have given us, we can only make suggestions, you need to decide on what makes the most sense based on your understanding of the data, the science behind it, and what questions you are trying to ask. You may also need to consult with an expert in the area and/or a professional statistician. Choosing to not do a beta regression because it is beyond you is like having your doctor say that you may need brain surgery, but he is going to take out your appendix instead because brains are beyond his experience, but he is good with appendixes.