I just want to confirm that I am understanding this correctly. So if logistic regression models have omitted variable bias, does that mean that I should discard any logistic regression models that does not include every significant main effects and their every significant interactions, even if I need to exclude some of the potentially significant interaction terms to avoid multicollinearity or to make an MCMC-GLM algorithm converge?
In my situation:
1. I am fitting a logistic regression model for my binary response against three predictors. When I run
R it does not seem to have any problem with this. However, when I try to run
MCMClogit(y~(A+B+C)^3) for a Bayesian power analysis on logistic regression model,
R tells me that the algorithm does not converge. The
MCMClogit algorithm cannot handle the model involving full interaction, meaning the Bayesian method is subject to omitted variable bias.
2. Because I was being so cautious about the omitted variable bias in logistic regression, I added bunch of interaction terms into my logistic regression model that deem to have significant effect on the response. This causes multicollinearity, which makes the p-values to become unreliable.
Does this mean that I should abandon this Bayesian approach of conducting power analysis? and does omitted variable bias mean that I should include every significant interaction even if it causes multicollinearity?