Lets say I want to regress a variable on a covariate which has distinct value zero but the all other values are following some smooth function? It could be e.g. Years of beeing a mom (once you are a mom you are very different from 0 years, i.e. the effect of going from 0 to 0.0001 year should be a jump, but from 0.0001 to 0.0002 sould be smooth). Or maybe exposre is 'Time of exposure to HPV' when we study cervix cancer?
One simple thing would be to add two covariates 'Years of being mom' and 'Are you a mom (yes/no)', but then all values would be 'No' exactly when the other variable is '0'.
Any ideas? Hierarchical model? If so, how?