Zero-inflated Poisson Regression for Continuous data

Question

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

Answer 1

Important takeaways for analysts:

1. Categorizing a continuous predictor will always result in a loss of information
2. "A lot of zeroes" is not 0 inflation, regardless of skew. I can find a negative binomial parametrization that can generate an arbitrary proportion of zeroes and an arbitrarily high maximum. 0 inflation is a theoretical process, like getting input from a broken Geiger counter: you have to know what's going on in the data
3. The usual way of handling real zero inflation is with a mixture model
4. Be especially cautious of truncation... that is when the instrument is not sensitive to detect values below a lower limit of detection and the result comes out to 0. An EM algorithm or Bayesian approach is needed
5. Zero-inflated Poisson is the most frequently cited zero-inflated model. It uses a mixture model for the 0s, and the Poisson GLM for the "non-zero part" (a misnomer because some of the positive-mean values may be 0)
6. You can have a zero-inflated "anything" model by using an EM fitter to iteratively predict the 0s that are 0-inflated and the effects for the non-0-inflated part
7. A Poisson GLM is completely reasonable for a continuous response provided: a) the log of the mean response is related to a linear combination of regressors and b) the variance is equal to the mean. But I gather this almost certainly not what you would have done, I think you were distracted by the oft cited 0 inflated Poisson model.