We are wondering whether it would be possible to use the same variable twice in a model: Once dichotomized, once continuous. The variable are questionnaire scores and participants are pre-screened to fall into extreme groups (so the middle is missing). The idea is that the two groups are qualitatively different from each other and do not represent a linear trend. To be precise, we expect a negative relationship with the DV in one group, but not in the other.
So we could model it using some non-linear model, but it might be difficult to interpret. If we use only the categorical variables we could compare these different groups well, but we lose all the variance in the predictor/questionnaire. So we were wondering if it is possible to get separate regression lines for each group by simply including the interaction of the two? It does feel very wrong to use the same variable twice. Also, it might be the same as using a quadratic predictor, maybe?
So the model would be DV = IVgrouped * IVcont.
Any thoughts? Thanks!