The question (from Quora):
Should I go through univariate analysis before running multivariate regression? For instance, if a single variable is not significant or ANOVA test tell me there is no relationship between my independent variable and binary outcome, should I exclude the variable from model? I found that sometimes variables insignificant in univariate analysis will become significant with other variables in my logistic model. I am not sure whether such variables should be included.
You have stated one of the reasons why you should not do what is called “bivariate screening” – that is, you should not automatically exclude variables that are not significant bivariately from a more complex model. In addition, those variable may act as important control variables or the fact that the effect sizes are small may be important in itself.
Good model building requires substantive knowledge and some intuition. No automatic method is going to be as good, although sometimes automatic methods are necessary (less often than many suppose, but still sometimes).