I an undertaking a binary logistic regression. I have created dummy variables out of a categorical variable and run them through the analysis. As expected, some of these categories are significant, whereas others are not. What I would like to know is, can I take just the significant categories and extract them to their own binary variables (where 1 is present and 0 is absent) so that I don't have to have a reference category, and I only have significant variables in my analysis? Does this make sense, or are these binary variables only valid when compared to a reference category?

Thanks for any clarification