# “Zero-inflated” predictors in regression?

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?

• I suggest you plot the two sets of fitted vs actual on the same plot (with y=x line marked lightly). You should see why quite quickly. If it doesn't show on that, try actual-fitted vs fitted on the same plot (with y=0 line marked in) – Glen_b Jul 1 '13 at 4:54
• There is no assumption for the distribution of the independent variables, but if you simply add that variable to your model you do assume linearity of its effect. If you have that many 0s, then it is reasonable to suspect that there is something special about that value, and you'll probably want to incorporate that in your model. Here is a discussion on how to do that: stats.stackexchange.com/questions/56306 – Maarten Buis Jul 1 '13 at 6:59
• @Maarten Buis: Thanks for the illuminating answer. Regarding the breastfeeding example with beta1 (for weeks breastfeeding) and beta2 (for non-breastfeeding) coefficients, suppose that the outcome is baby health: If I get a significant beta1 (e.g. P=0.001) and a non-significant beta2 (e.g. P=0.1), should I interpret the result that more breastfeeding is good for the baby but non-breastfeeding does not affect the baby? – KuJ Jul 2 '13 at 4:20
• In my example $\beta_1$ refers to the linear effect, while $\beta_2$ refers to the discrete jump at 0. So, the null hypothesis for the second test is that there is no discrete jump, i.e. you could just as well describe the relationship with just a linear effect. With the $p$-values you report you cannot reject that hypothesis. – Maarten Buis Jul 2 '13 at 6:39
• @ Maarten Buis: Recently I find that your suggestion is implemented in an article “On the implication of structural zeros as independent variables in regression analysis: applications to alcohol research (ncbi.nlm.nih.gov/pmc/articles/PMC5628625)”. – KuJ Feb 22 '18 at 1:56