I have a zero-inflated continuous dependent variable for which I would like to be able to perform a quantile regression analysis. Approximately half of the observations are true zeros, and the remainder of the values vary widely and are highly right-skewed. I first attempted to conduct a multivariable quantile regression analysis using the 0.1, 0.25, 0.5, 0.75, and 0.9 quantiles. Given the amount of zeros, I was unable to obtain estimates for the 0.1 and 0.25 quantiles.
I’m wondering if I can use a two-part model to first model, using a logit or probit link, the odds of values >0 occurring, and then using quantile regression analysis to estimate the effect of my independent variables across the distribution of the values >0. So far I’ve only found approaches to dealing with zero-inflation for count data. I found the Stata package “twopm”, which provides methods for two-part models on continuous data, but only using glm approaches (lm or Gamma). I know that this is possible, as I found this dissertation, which uses the approach I would like to use (although I haven’t been able to figure out how to get my hands on the full text). Would anyone be able to point me in the direction for conducting a two-part model that includes a quantile regression approach using R or Stata?
Any help would be greatly appreciated. Thank you.