I have a continuous variable that I'm trying to model but have a number of issues. The variable is continuous, positive, right skewed and has a large zero-inflation. Whilst the formulation of the score means that they are technically continuous, in practice they are measured (and rounded), results are typically more categorical in nature. In addition, the zero inflation is part of the process and is a well documented phenomenon.
I have seen some conflicting advice for how to model this. I've tried modelling by categorising the variable into groups and model using a zero-inflated Poisson regression. But I'm told that categorising is the wrong thing to do, and to model it as continuously. I've thought about modelling using a hurdle model (Gamma/Lognormal with binomial for zeroes) however the assumption there is that zero isn't part of the data generation process and that the zeroes are a separate process which seems to violate the above.
Any advice about the best way to model this data, with any references to support it would be great.
Thanks in advance