I know that zero-inflated models (e.g. zero-inflated Poisson or negative binomial models) can be used for dependent variables. I also know that in general there are no assumptions for the independent variables (i.e. predictors) in regression analyses. However, I have a quantitative (continuous or count) predictor which has many (say, 40-60%) zeros. When I used it as a quantitative predictor in regression (linear or logistic) I got a small P value (i.e. P<0.01), but when I used it as a binary predictor (zero or not) I got a P value>0.05. Why did it happen? How do I interpret this result?