Three out of five of my covariates in my logistic model are significant but can only find explanation/ interpretation for one of the significant ones. Should I only discuss the one and leave out the two?
If the "unexplained" ones are simply mysterious but still plausible you could still talk about them and say "we are not sure" ... but if some of the significant signs are counter-intuitive (wrong direction) I think there has to be a serious re-think of what is going on. How well would the model work WITH JUST THE ONE significant explanatory variable. Can you test for the significant improvement in fit with the addition of more (unexplained) variables? Is there correlation between your effects? Something like the methodology of "step wise" entry would perhaps allow you to see truly significant effects/
I would recommend further exploration with the model.
I would not recommend hiding anything you find -- if you find it you either have to explain it or discount it as irrelevant. For example what are the sizes of the t-statistics?
The correlation matrix of the independent variables can give a lot of information.
Some of the independent variables can not be statistically significant, but all the model must be statustically significant and the percentage of corretly classified cases must be greater than 75% (Hair et al, 2010).
You can use two or three logistic models with some on the independent variables and one model with all the variables.
A bivariate analysis can be useful before multivariate analysis.
You can use chi- square test of independence to test if the dependent variable is independent to each of the independent variable.