Continuous dependent variable between 0 and 1 fitted with sigmoidal function I've tried to find an answer to this to no avail. It is similar to this question, but not quite identical.
I have a continuous dependent variable that occurs between zero and one (with some data points landing precisely on zero and one). I want to fit a $S$-shaped regression. My data is on coral reefs and the $Y$ variable is percentage dead per m$^2$. I don't have frequency counts in terms of successes and failures, just percentage mortality by cover.
Is logit a terrible idea here? Since I only have two sig-figs would turning 80% mortality into 80 out of 100 observations be a bad idea? Is there some other sigmoidal function I might explore?
 A: I don't think beta regression, as suggested by @O_Devinyak, will work well for this case as there are exact 0s and 1s in the data and the beta distribution only works for values between, but not including, 0 and 1. 
A solution that has become more popular in economics is the so-called fractional logit model, which economists tend to attribute to Papke and Wooldridge (1996), though the basic idea can be traced back to at least Wedderburn (1974). Nowadays it is fairly easy to estimate such models. For example in Stata (the statistical program I know best) you would use the glm program in combination with the link(logit) family(binomial) vce(robust) options. 
Wedderburn, R. W. 1974. Quasi-likelihood functions, generalized linear models, and the Gauss—Newton method. Biometrika, 61(3): 439-447.
Papke, Leslie E. and Jeffrey M. Wooldridge. 1996. Econometric methods for fractional response variables with an application to 401(k) Plan participation rates. Journal of Applied Econometrics, 11(6): 619-632. 
