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I am using penalised methods based on glmnet package in R. I used the zero inflated Poisson regression for my sample which contains 2,734 observations and 27 predictors. There is a high level of multicollinearity among the predictors. I would like to identify a sparse subset of predictors, so I am considering elastic net penalized methods to select these features.

My question is: can I used penalised methods just for selection in a regular Poisson GLM and then estimate the zero-inflated Poisson regression model using the features identified in the earlier model?

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Nope! The Poisson model is a biased estimate of the true model if you have zero-inflation. Depending on the strength of the relationship between the 0-process and the predictor(s) you can induce bias of any magnitude in the Poisson coefficient estimates. The penalty will be applied to the wrong coefficients. You'll have to devise a method to select a sparse model with the zero-inflated Poisson model.

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