Variables significant when changing reference category? I'm doing a research about risk tolerance and demographic factors using a logistic regression.
When I first included generation (Z Y X BB) in my model with the baseline of BB, Z Y X yield insignificant result. When I changed the reference category to Z, the other generations: Y X BB were all significant at 1%.
Can anyone tell me why and how should I deal with this problem?
 A: This represents the (somewhat confusing) way that regression results involving multi-level categorical predictors are typically reported.
Your regression evidently used treatment coding for the 4-level categorical predictor generation. That chooses one level of the predictor as a reference. The reported regression coefficients (and their p-values) then are for differences of each of the other levels from that particular reference level. So it's not surprising that the individual significance indicators change as you change the reference level.*
This way of reporting results for individual levels of the predictor doesn't represent the overall significance of generation, including all 4 of its levels. That's probably what you're most interested in. For that you need to compare a model that includes all the predictors against one in which you have removed generation completely, and see if the models are significantly different. That's typically done with an analysis of variance comparison between the two models. If you thus find generation to be significant overall then you can use standard post-hoc tests to compare among the individual levels.

*I am a bit surprised that "BB" was significant when "Z" was the reference but "Z" wasn't when "BB" was the reference. Hard to say what's going on without more details about the rest of your model, in particular any interaction terms.
